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0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(November 9, 2009)] TJ ET 0.267 0.267 0.267 rg BT 26.250 663.247 Td /F1 9.8 Tf [(Nedialko Dimitrov)] TJ ET 0.271 0.267 0.267 rg BT 102.632 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 108.053 663.247 Td /F1 9.8 Tf [(Sebastian Goll)] TJ ET 0.271 0.267 0.267 rg BT 171.457 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 176.878 663.247 Td /F1 9.8 Tf [(Nathaniel Hupert)] TJ ET 0.271 0.267 0.267 rg BT 250.032 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 255.453 663.247 Td /F1 9.8 Tf [(Babak Pourbohloul)] TJ ET 0.271 0.267 0.267 rg BT 337.831 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 343.252 663.247 Td /F1 9.8 Tf [(Lauren Meyers)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Dimitrov N, Goll S, Hupert N, Pourbohloul B, Meyers L. Optimizing Tactics for use of the U.S. Antiviral Strategic National )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(Stockpile for Pandemic \(H1N1\) Influenza, 2009. PLOS Currents Influenza. 2009 Nov 9 . Edition 1. doi: )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(10.1371/currents.RRN1127.)] TJ ET q 15.000 35.720 577.500 589.432 re W n 0.271 0.267 0.267 rg BT 26.250 598.430 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(Public health agencies across the globe are working to mitigate the impact of the 2009 pandemic caused by swine-origin )] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(influenza A \(H1N1\) virus. Prior to the large-scale distribution of an effective vaccine, the primary modes of control have included )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(careful surveillance, social distancing and hygiene measures, strategic school closures, other community measures, and the )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(prudent use of antiviral medications to prevent infection \(prophylaxis\) or reduce the severity and duration of symptoms )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(\(treatment\). Here, we use mathematical models to determine the optimal geo-temporal tactics for distributing the U.S. strategic )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(national stockpile of antivirals for treatment of infected cases during the early stages of a pandemic, prior to the wide availability )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(of vaccines.)] TJ ET BT 26.250 487.643 Td /F1 9.8 Tf [(We present a versatile optimization method for efficiently searching large sets of public health intervention strategies, and apply )] TJ ET BT 26.250 475.738 Td /F1 9.8 Tf [(it to evaluating tactics for distributing antiviral medications from the U.S. Strategic National Stockpile \(SNS\). We implemented )] TJ ET BT 26.250 463.833 Td /F1 9.8 Tf [(the algorithm on a network model of H1N1 transmission within and among U.S. cities to project the epidemiological impacts of )] TJ ET BT 26.250 451.929 Td /F1 9.8 Tf [(antiviral stockpile distribution schedules and priorities. The resulting optimized strategies critically depend on the rates of )] TJ ET BT 26.250 440.024 Td /F1 9.8 Tf [(antiviral uptake and wastage \(through misallocation or loss\). And while a surprisingly simple pro rata distribution schedule is )] TJ ET BT 26.250 428.119 Td /F1 9.8 Tf [(competitive with the optimized strategies across a wide range of uptake and wastage, other equally simple policies perform )] TJ ET BT 26.250 416.214 Td /F1 9.8 Tf [(poorly.)] TJ ET BT 26.250 396.810 Td /F1 9.8 Tf [(Even as vaccination campaigns get underway worldwide, antiviral medications continue to play a critical in reducing H1N1-)] TJ ET BT 26.250 384.905 Td /F1 9.8 Tf [(associated morbidity and mortality. If efforts are made to increase the fraction of cases treated promptly with antivirals above )] TJ ET BT 26.250 373.000 Td /F1 9.8 Tf [(current levels, our model suggests that optimal use of the antiviral component of the Strategic National Stockpile may )] TJ ET BT 26.250 361.095 Td /F1 9.8 Tf [(appreciably slow the transmission of H1N1 during fall 2009, thereby improving the impact of targeted vaccination. A more )] TJ ET BT 26.250 349.191 Td /F1 9.8 Tf [(aggressive optimized antiviral strategy of this type may prove critical to mitigating future flu pandemics, but may increase the )] TJ ET BT 26.250 337.286 Td /F1 9.8 Tf [(risk of antiviral resistance.)] TJ ET BT 26.250 300.683 Td /F4 12.0 Tf [(Author Summary)] TJ ET BT 26.250 280.729 Td /F1 9.8 Tf [(The U.S. Government holds millions of treatment courses of antiviral medications its Strategic National Stockpile \(SNS\), but )] TJ ET BT 26.250 268.824 Td /F1 9.8 Tf [(there are no published criteria for sequential release of these medications to States and Territories during the course of a )] TJ ET BT 26.250 256.920 Td /F1 9.8 Tf [(worldwide influenza pandemic, such as the one currently caused by the pandemic influenza A \(H1N1\) virus.. We employed )] TJ ET BT 26.250 245.015 Td /F1 9.8 Tf [(advanced optimization methods to evaluate millions of antiviral distribution schedules that vary in both the amount of each )] TJ ET BT 26.250 233.110 Td /F1 9.8 Tf [(release and whether allocations to states are proportional to overall population or recent flu activity. We find that, for the case of )] TJ ET BT 26.250 221.205 Td /F1 9.8 Tf [(2009 \(H1N1\) pandemic flu, a simple distribution schedule of periodic small releases proportional to state population densities is )] TJ ET BT 26.250 209.301 Td /F1 9.8 Tf [(a near-optimal policy. For this antiviral distribution scheme to have an impact on transmission of the current H1N1 virus, )] TJ ET BT 26.250 197.396 Td /F1 9.8 Tf [(however, a higher proportion of cases must be identified and treated promptly with antivirals than is currently the case. This )] TJ ET BT 26.250 185.491 Td /F1 9.8 Tf [(paper provides both practical guidance for future flu intervention and new methods that are readily adaptable to optimizing a )] TJ ET BT 26.250 173.586 Td /F1 9.8 Tf [(broad range of infectious disease control policies.)] TJ ET BT 26.250 136.984 Td /F4 12.0 Tf [(Introduction)] TJ ET Q q 15.000 684.354 577.500 53.646 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Optimizing Tactics for use of the U.S. Antiviral Strategic )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(National Stockpile for Pandemic \(H1N1\) Influenza, 2009)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(November 9, 2009)] TJ ET 0.267 0.267 0.267 rg BT 26.250 663.247 Td /F1 9.8 Tf [(Nedialko Dimitrov)] TJ ET 0.271 0.267 0.267 rg BT 102.632 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 108.053 663.247 Td /F1 9.8 Tf [(Sebastian Goll)] TJ ET 0.271 0.267 0.267 rg BT 171.457 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 176.878 663.247 Td /F1 9.8 Tf [(Nathaniel Hupert)] TJ ET 0.271 0.267 0.267 rg BT 250.032 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 255.453 663.247 Td /F1 9.8 Tf [(Babak Pourbohloul)] TJ ET 0.271 0.267 0.267 rg BT 337.831 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 343.252 663.247 Td /F1 9.8 Tf [(Lauren Meyers)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Dimitrov N, Goll S, Hupert N, Pourbohloul B, Meyers L. Optimizing Tactics for use of the U.S. Antiviral Strategic National )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(Stockpile for Pandemic \(H1N1\) Influenza, 2009. PLOS Currents Influenza. 2009 Nov 9 . Edition 1. doi: )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(10.1371/currents.RRN1127.)] TJ ET q 15.000 35.720 577.500 589.432 re W n 0.271 0.267 0.267 rg BT 26.250 598.430 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(Public health agencies across the globe are working to mitigate the impact of the 2009 pandemic caused by swine-origin )] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(influenza A \(H1N1\) virus. Prior to the large-scale distribution of an effective vaccine, the primary modes of control have included )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(careful surveillance, social distancing and hygiene measures, strategic school closures, other community measures, and the )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(prudent use of antiviral medications to prevent infection \(prophylaxis\) or reduce the severity and duration of symptoms )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(\(treatment\). Here, we use mathematical models to determine the optimal geo-temporal tactics for distributing the U.S. strategic )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(national stockpile of antivirals for treatment of infected cases during the early stages of a pandemic, prior to the wide availability )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(of vaccines.)] TJ ET BT 26.250 487.643 Td /F1 9.8 Tf [(We present a versatile optimization method for efficiently searching large sets of public health intervention strategies, and apply )] TJ ET BT 26.250 475.738 Td /F1 9.8 Tf [(it to evaluating tactics for distributing antiviral medications from the U.S. Strategic National Stockpile \(SNS\). We implemented )] TJ ET BT 26.250 463.833 Td /F1 9.8 Tf [(the algorithm on a network model of H1N1 transmission within and among U.S. cities to project the epidemiological impacts of )] TJ ET BT 26.250 451.929 Td /F1 9.8 Tf [(antiviral stockpile distribution schedules and priorities. The resulting optimized strategies critically depend on the rates of )] TJ ET BT 26.250 440.024 Td /F1 9.8 Tf [(antiviral uptake and wastage \(through misallocation or loss\). And while a surprisingly simple pro rata distribution schedule is )] TJ ET BT 26.250 428.119 Td /F1 9.8 Tf [(competitive with the optimized strategies across a wide range of uptake and wastage, other equally simple policies perform )] TJ ET BT 26.250 416.214 Td /F1 9.8 Tf [(poorly.)] TJ ET BT 26.250 396.810 Td /F1 9.8 Tf [(Even as vaccination campaigns get underway worldwide, antiviral medications continue to play a critical in reducing H1N1-)] TJ ET BT 26.250 384.905 Td /F1 9.8 Tf [(associated morbidity and mortality. If efforts are made to increase the fraction of cases treated promptly with antivirals above )] TJ ET BT 26.250 373.000 Td /F1 9.8 Tf [(current levels, our model suggests that optimal use of the antiviral component of the Strategic National Stockpile may )] TJ ET BT 26.250 361.095 Td /F1 9.8 Tf [(appreciably slow the transmission of H1N1 during fall 2009, thereby improving the impact of targeted vaccination. A more )] TJ ET BT 26.250 349.191 Td /F1 9.8 Tf [(aggressive optimized antiviral strategy of this type may prove critical to mitigating future flu pandemics, but may increase the )] TJ ET BT 26.250 337.286 Td /F1 9.8 Tf [(risk of antiviral resistance.)] TJ ET BT 26.250 300.683 Td /F4 12.0 Tf [(Author Summary)] TJ ET BT 26.250 280.729 Td /F1 9.8 Tf [(The U.S. Government holds millions of treatment courses of antiviral medications its Strategic National Stockpile \(SNS\), but )] TJ ET BT 26.250 268.824 Td /F1 9.8 Tf [(there are no published criteria for sequential release of these medications to States and Territories during the course of a )] TJ ET BT 26.250 256.920 Td /F1 9.8 Tf [(worldwide influenza pandemic, such as the one currently caused by the pandemic influenza A \(H1N1\) virus.. We employed )] TJ ET BT 26.250 245.015 Td /F1 9.8 Tf [(advanced optimization methods to evaluate millions of antiviral distribution schedules that vary in both the amount of each )] TJ ET BT 26.250 233.110 Td /F1 9.8 Tf [(release and whether allocations to states are proportional to overall population or recent flu activity. We find that, for the case of )] TJ ET BT 26.250 221.205 Td /F1 9.8 Tf [(2009 \(H1N1\) pandemic flu, a simple distribution schedule of periodic small releases proportional to state population densities is )] TJ ET BT 26.250 209.301 Td /F1 9.8 Tf [(a near-optimal policy. For this antiviral distribution scheme to have an impact on transmission of the current H1N1 virus, )] TJ ET BT 26.250 197.396 Td /F1 9.8 Tf [(however, a higher proportion of cases must be identified and treated promptly with antivirals than is currently the case. This )] TJ ET BT 26.250 185.491 Td /F1 9.8 Tf [(paper provides both practical guidance for future flu intervention and new methods that are readily adaptable to optimizing a )] TJ ET BT 26.250 173.586 Td /F1 9.8 Tf [(broad range of infectious disease control policies.)] TJ ET BT 26.250 136.984 Td /F4 12.0 Tf [(Introduction)] TJ ET Q q 15.000 684.354 577.500 53.646 re W n 0.267 0.267 0.267 rg BT 15.000 718.042 Td /F2 21.0 Tf [(Optimizing Tactics for use of the U.S. Antiviral Strategic )] TJ ET BT 15.000 693.094 Td /F2 21.0 Tf [(National Stockpile for Pandemic \(H1N1\) Influenza, 2009)] TJ ET Q 0.271 0.267 0.267 rg BT 15.000 675.088 Td /F3 9.8 Tf [(November 9, 2009)] TJ ET 0.267 0.267 0.267 rg BT 26.250 663.247 Td /F1 9.8 Tf [(Nedialko Dimitrov)] TJ ET 0.271 0.267 0.267 rg BT 102.632 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 108.053 663.247 Td /F1 9.8 Tf [(Sebastian Goll)] TJ ET 0.271 0.267 0.267 rg BT 171.457 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 176.878 663.247 Td /F1 9.8 Tf [(Nathaniel Hupert)] TJ ET 0.271 0.267 0.267 rg BT 250.032 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 255.453 663.247 Td /F1 9.8 Tf [(Babak Pourbohloul)] TJ ET 0.271 0.267 0.267 rg BT 337.831 663.247 Td /F1 9.8 Tf [(, )] TJ ET 0.267 0.267 0.267 rg BT 343.252 663.247 Td /F1 9.8 Tf [(Lauren Meyers)] TJ ET 0.271 0.267 0.267 rg BT 26.250 651.342 Td /F1 9.8 Tf [(Dimitrov N, Goll S, Hupert N, Pourbohloul B, Meyers L. Optimizing Tactics for use of the U.S. Antiviral Strategic National )] TJ ET BT 26.250 639.438 Td /F1 9.8 Tf [(Stockpile for Pandemic \(H1N1\) Influenza, 2009. PLOS Currents Influenza. 2009 Nov 9 . Edition 1. doi: )] TJ ET BT 26.250 627.533 Td /F1 9.8 Tf [(10.1371/currents.RRN1127.)] TJ ET q 15.000 35.720 577.500 589.432 re W n 0.271 0.267 0.267 rg BT 26.250 598.430 Td /F4 12.0 Tf [(Abstract)] TJ ET BT 26.250 578.476 Td /F1 9.8 Tf [(Public health agencies across the globe are working to mitigate the impact of the 2009 pandemic caused by swine-origin )] TJ ET BT 26.250 566.571 Td /F1 9.8 Tf [(influenza A \(H1N1\) virus. Prior to the large-scale distribution of an effective vaccine, the primary modes of control have included )] TJ ET BT 26.250 554.667 Td /F1 9.8 Tf [(careful surveillance, social distancing and hygiene measures, strategic school closures, other community measures, and the )] TJ ET BT 26.250 542.762 Td /F1 9.8 Tf [(prudent use of antiviral medications to prevent infection \(prophylaxis\) or reduce the severity and duration of symptoms )] TJ ET BT 26.250 530.857 Td /F1 9.8 Tf [(\(treatment\). Here, we use mathematical models to determine the optimal geo-temporal tactics for distributing the U.S. strategic )] TJ ET BT 26.250 518.952 Td /F1 9.8 Tf [(national stockpile of antivirals for treatment of infected cases during the early stages of a pandemic, prior to the wide availability )] TJ ET BT 26.250 507.048 Td /F1 9.8 Tf [(of vaccines.)] TJ ET BT 26.250 487.643 Td /F1 9.8 Tf [(We present a versatile optimization method for efficiently searching large sets of public health intervention strategies, and apply )] TJ ET BT 26.250 475.738 Td /F1 9.8 Tf [(it to evaluating tactics for distributing antiviral medications from the U.S. Strategic National Stockpile \(SNS\). We implemented )] TJ ET BT 26.250 463.833 Td /F1 9.8 Tf [(the algorithm on a network model of H1N1 transmission within and among U.S. cities to project the epidemiological impacts of )] TJ ET BT 26.250 451.929 Td /F1 9.8 Tf [(antiviral stockpile distribution schedules and priorities. The resulting optimized strategies critically depend on the rates of )] TJ ET BT 26.250 440.024 Td /F1 9.8 Tf [(antiviral uptake and wastage \(through misallocation or loss\). And while a surprisingly simple pro rata distribution schedule is )] TJ ET BT 26.250 428.119 Td /F1 9.8 Tf [(competitive with the optimized strategies across a wide range of uptake and wastage, other equally simple policies perform )] TJ ET BT 26.250 416.214 Td /F1 9.8 Tf [(poorly.)] TJ ET BT 26.250 396.810 Td /F1 9.8 Tf [(Even as vaccination campaigns get underway worldwide, antiviral medications continue to play a critical in reducing H1N1-)] TJ ET BT 26.250 384.905 Td /F1 9.8 Tf [(associated morbidity and mortality. If efforts are made to increase the fraction of cases treated promptly with antivirals above )] TJ ET BT 26.250 373.000 Td /F1 9.8 Tf [(current levels, our model suggests that optimal use of the antiviral component of the Strategic National Stockpile may )] TJ ET BT 26.250 361.095 Td /F1 9.8 Tf [(appreciably slow the transmission of H1N1 during fall 2009, thereby improving the impact of targeted vaccination. A more )] TJ ET BT 26.250 349.191 Td /F1 9.8 Tf [(aggressive optimized antiviral strategy of this type may prove critical to mitigating future flu pandemics, but may increase the )] TJ ET BT 26.250 337.286 Td /F1 9.8 Tf [(risk of antiviral resistance.)] TJ ET BT 26.250 300.683 Td /F4 12.0 Tf [(Author Summary)] TJ ET BT 26.250 280.729 Td /F1 9.8 Tf [(The U.S. Government holds millions of treatment courses of antiviral medications its Strategic National Stockpile \(SNS\), but )] TJ ET BT 26.250 268.824 Td /F1 9.8 Tf [(there are no published criteria for sequential release of these medications to States and Territories during the course of a )] TJ ET BT 26.250 256.920 Td /F1 9.8 Tf [(worldwide influenza pandemic, such as the one currently caused by the pandemic influenza A \(H1N1\) virus.. We employed )] TJ ET BT 26.250 245.015 Td /F1 9.8 Tf [(advanced optimization methods to evaluate millions of antiviral distribution schedules that vary in both the amount of each )] TJ ET BT 26.250 233.110 Td /F1 9.8 Tf [(release and whether allocations to states are proportional to overall population or recent flu activity. We find that, for the case of )] TJ ET BT 26.250 221.205 Td /F1 9.8 Tf [(2009 \(H1N1\) pandemic flu, a simple distribution schedule of periodic small releases proportional to state population densities is )] TJ ET BT 26.250 209.301 Td /F1 9.8 Tf [(a near-optimal policy. For this antiviral distribution scheme to have an impact on transmission of the current H1N1 virus, )] TJ ET BT 26.250 197.396 Td /F1 9.8 Tf [(however, a higher proportion of cases must be identified and treated promptly with antivirals than is currently the case. This )] TJ ET BT 26.250 185.491 Td /F1 9.8 Tf [(paper provides both practical guidance for future flu intervention and new methods that are readily adaptable to optimizing a )] TJ ET BT 26.250 173.586 Td /F1 9.8 Tf [(broad range of infectious disease control policies.)] TJ ET BT 26.250 136.984 Td /F4 12.0 Tf [(Introduction)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(1)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 8 0 obj << /Type /Font /Subtype /Type1 /Name /F1 /BaseFont /Helvetica /Encoding /WinAnsiEncoding >> endobj 9 0 obj << /Type /Font /Subtype /Type1 /Name /F2 /BaseFont /Times-Bold /Encoding /WinAnsiEncoding >> endobj 10 0 obj << /Type /Font /Subtype /Type1 /Name /F3 /BaseFont /Times-Italic /Encoding /WinAnsiEncoding >> endobj 11 0 obj << /Type /Font /Subtype /Type1 /Name /F4 /BaseFont /Helvetica-Bold /Encoding /WinAnsiEncoding >> endobj 12 0 obj << /Type /XObject /Subtype /Image /Width 500 /Height 52 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 500 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 144>> stream x1 0 'ݲ؎"e{dzAdzAdzAdzAdzAdzAdzAdzAdzAdzAdzAdzAtlM0\ endstream endobj 13 0 obj << /Type /XObject /Subtype /Image /Width 500 /Height 52 /SMask 12 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 500 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 3574>> stream x}ƕK*8+0T ֮ S L*0߇d" sl2FBiFwY0 00 0ŝa0 aqgR܋x||lu2 03UL۶BxI 0:UU0x;֝($z%șHڶ ÐVz ]IS> â(.* TQUuL5 $>BvpH0U:xkkGJT{OɗRNyGOΙyn)q7`(~_Ji2vgk]qVꔷ3N'ȴy4Ikm6!q:FJ)-0n܋v!^}_Z l61va_~Bxw8mv;EJY8}zzQ3]Pȹ,2_jfY4MQ[ '.uO O͋kշ9b6.#ߦUUzhf09+nKɿ4 f7Bu7ĨMfrF0`s8429j1}ZWDW;A4ҫ'TQ{7Cb[$ -"ΨMQgzN/2R7Tco*W:N݋6TUu8`RSi O>r;z^m(0w`:m=]գCE&t |ZYQ%{X[nR+zbEFΧ5pzq`ުం Ih{9G 4wMx' nmvEZ sg7?ZQ}&ҎKGuPu.j8UgNKꓙQC)s#$1䧈x[Z(|Xzc;t<~50Hh_T3Ur>a$]B8Fz[?K>Y/rQ=E4?EaLqzpX!(nNut]}e(/S\fz,<ZOEa]0 sCS_}I Y}n۶r(fg7#)h6ա}$ üvq]Aא$c0ddBDQ)ueypU-z~9Hk<$I©y'Tk`yY d}e{䨙ǐu>&w񚓶('GI\rm[G4 Sk7$B pEkYYC/ 9&Ʋ[V9MQ':X|C֨ʉ jt"ޡ+rttBռGdiM FuTEi(łv]fk"8Ldp' ^הMup2`M?dE!|KJ-\.MzکC=&¾HfR7$ev,La0+$OFuEQ"i,ːN?~E*t4qΚF:t`,{RkR]ޜ(Ԕѣ$IbN}5لS1(Ȱ$I$(eWp8Lٱ3߯ky۶&. 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66 0 R 68 0 R 70 0 R 76 0 R 80 0 R 82 0 R 84 0 R 86 0 R 88 0 R 90 0 R 92 0 R 98 0 R 102 0 R 104 0 R 106 0 R 108 0 R 110 0 R 112 0 R 114 0 R 120 0 R ] /Contents 57 0 R >> endobj 57 0 obj << /Length 21887 >> stream 0.271 0.267 0.267 rg q 15.000 109.220 577.500 667.780 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(In March/April 2009, a new swine-origin strain of influenza A/H1N1 virus emerged into human populations in California and )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(Mexico and has since escalated into a pandemic. The U.S. experienced low levels of sustained H1N1 transmission throughout )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(the summer months of 2009, and in the Southern hemisphere the novel virus largely displaced seasonal influenza, causing )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(more severe morbidity in a younger adults and children than is typical with the flu. Starting in September, the U.S. began to )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(experience large geo-temporally distinct outbreaks of influenza like illness and confirmed H1N1 disease in States and )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(Territories. As of mid-October, total cases reported by surveillance systems as well as pediatric deaths had surpassed levels )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(typically seen for the entire flu season ending in mid-Spring 2010.)] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(During the early weeks of the epidemic, the U.S. Centers for Disease Control and Prevention \(CDC\) distributed 11 million of the )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(50 million antiviral treatment courses from the federally held portion of the national antiviral stockpile. This distribution went to )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(States and Territories \(as well as to four large cities\) on a pro rata basis \(that is, in proportion to population size\). Since the )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(recipients had local stockpiles as well, this allowed the CDC to exceeded the pre-determined target of distribution of 31 million )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(treatment courses of oseltamivir and zanamivir prior to the acceleration phase of the pandemic )] TJ ET 0.267 0.267 0.267 rg BT 436.462 629.024 Td /F1 9.8 Tf [([1])] TJ ET 0.271 0.267 0.267 rg BT 447.304 629.024 Td /F1 9.8 Tf [( . With additional purchases, )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(the Federal stockpile now remains at approximately 50 million treatment courses, but there is no clear quantitative guidance to )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(indicate the optimal use of these countermeasures.)] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(Key policy statements have called for the use of mathematical models to support the development of an evidence-based policy )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(for e?ectively deploying the remaining antiviral stockpile and other limited or costly measures to limit morbidity and mortality )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(from H1N1 )] TJ ET 0.267 0.267 0.267 rg BT 76.092 562.000 Td /F1 9.8 Tf [([2])] TJ ET BT 86.934 562.000 Td /F1 9.8 Tf [([3])] TJ ET 0.271 0.267 0.267 rg BT 97.776 562.000 Td /F1 9.8 Tf [( . While mathematical modelers have taken great strides towards building predictive models of disease )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(transmission dynamics within human populations, the computational complexity of these models often precludes systematic )] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(optimization of the demographic, spatial and temporal distribution of costly resources. Thus the typical approach has been to )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(evaluate a relatively small set of candidate strategies )] TJ ET 0.267 0.267 0.267 rg BT 257.101 526.286 Td /F1 9.8 Tf [([4])] TJ ET BT 267.943 526.286 Td /F1 9.8 Tf [([5])] TJ ET BT 278.785 526.286 Td /F1 9.8 Tf [([6])] TJ ET BT 289.627 526.286 Td /F1 9.8 Tf [([7])] TJ ET 0.271 0.267 0.267 rg BT 300.469 526.286 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 506.881 Td /F1 9.8 Tf [(Here, we use a new algorithm that efficiently searches large strategy spaces to analyze the optimal use of the U.S. antiviral )] TJ ET BT 26.250 494.976 Td /F1 9.8 Tf [(stockpile against pandemic influenza prior to widespread and effective vaccination. We assume, in line with CDC guidance, that )] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(antivirals will be used exclusively for treatment of symptomatic individuals rather than wide scale pre-exposure prophylaxis. We )] TJ ET BT 26.250 471.167 Td /F1 9.8 Tf [(apply our algorithm to a U.S. national-scale network model of H1N1 transmission that is based on demographic and travel data )] TJ ET BT 26.250 459.262 Td /F1 9.8 Tf [(from the U.S. Census Bureau and the Bureau of Transportation Statistics and assumes disease parameters estimated for H1N1 )] TJ ET BT 26.250 447.357 Td /F1 9.8 Tf [(during the initial March-April 2009 outbreak in Mexico City.)] TJ ET BT 26.250 410.755 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 390.801 Td /F1 9.8 Tf [(We couple a fast, scalable, and adaptable optimization algorithm to a detailed simulation model of influenza transmission within )] TJ ET BT 26.250 378.896 Td /F1 9.8 Tf [(and among the 100 largest cities in the United States. In brief, the method involves running many stochastic simulations of )] TJ ET BT 26.250 366.991 Td /F1 9.8 Tf [(H1N1 transmission, each requiring an intervention policy as an argument. The optimization algorithm dictates the choice of )] TJ ET BT 26.250 355.086 Td /F1 9.8 Tf [(intervention policy for each simulation, with the goal of identifying the optimal intervention policy given the highly stochastic )] TJ ET BT 26.250 343.182 Td /F1 9.8 Tf [(simulation output.)] TJ ET BT 26.250 306.579 Td /F4 12.0 Tf [(Optimization method)] TJ ET BT 26.250 285.349 Td /F1 9.8 Tf [(A time-based intervention policy is a series of actions )] TJ ET q 73.500 0 0 13.500 258.173 282.649 cm /I4 Do Q BT 331.673 285.349 Td /F1 9.8 Tf [( taken in sequence over )] TJ ET q 11.250 0 0 10.500 437.899 285.649 cm /I6 Do Q BT 449.149 285.349 Td /F1 9.8 Tf [( time periods \(Fig. 1\). Our )] TJ ET BT 26.250 273.125 Td /F1 9.8 Tf [(objective is to rapidly search large sets of time-based intervention policies to ?nd those that will be most e?ective at achieving a )] TJ ET BT 26.250 261.220 Td /F1 9.8 Tf [(public health goal, such as limiting morbidity and mortality associated with in?uenza. To achieve this, we use trees to represent )] TJ ET BT 26.250 249.315 Td /F1 9.8 Tf [(all possible policies \(Fig. 1\). The ?rst \(highest\) level of a policy tree is a single node attached to several edges; each of those )] TJ ET BT 26.250 237.411 Td /F1 9.8 Tf [(edges corresponds to one of the possible actions in the first time period and leads to a level-two node. Similarly each level-two )] TJ ET BT 26.250 225.506 Td /F1 9.8 Tf [(node is attached to edges corresponding to all possible actions during the second time period, and so on. Each intervention )] TJ ET BT 26.250 213.601 Td /F1 9.8 Tf [(policy corresponds to a unique path through the tree.)] TJ ET 0.965 0.965 0.965 rg 26.250 109.220 555.000 94.500 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 203.720 m 581.250 203.720 l 581.250 202.970 l 26.250 202.970 l f q 225.000 0 0 78.750 35.250 115.220 cm /I8 Do Q q 35.250 109.220 537.000 0.000 re W n Q Q q 15.000 109.220 577.500 667.780 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(In March/April 2009, a new swine-origin strain of influenza A/H1N1 virus emerged into human populations in California and )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(Mexico and has since escalated into a pandemic. The U.S. experienced low levels of sustained H1N1 transmission throughout )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(the summer months of 2009, and in the Southern hemisphere the novel virus largely displaced seasonal influenza, causing )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(more severe morbidity in a younger adults and children than is typical with the flu. Starting in September, the U.S. began to )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(experience large geo-temporally distinct outbreaks of influenza like illness and confirmed H1N1 disease in States and )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(Territories. As of mid-October, total cases reported by surveillance systems as well as pediatric deaths had surpassed levels )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(typically seen for the entire flu season ending in mid-Spring 2010.)] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(During the early weeks of the epidemic, the U.S. Centers for Disease Control and Prevention \(CDC\) distributed 11 million of the )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(50 million antiviral treatment courses from the federally held portion of the national antiviral stockpile. This distribution went to )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(States and Territories \(as well as to four large cities\) on a pro rata basis \(that is, in proportion to population size\). Since the )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(recipients had local stockpiles as well, this allowed the CDC to exceeded the pre-determined target of distribution of 31 million )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(treatment courses of oseltamivir and zanamivir prior to the acceleration phase of the pandemic )] TJ ET 0.267 0.267 0.267 rg BT 436.462 629.024 Td /F1 9.8 Tf [([1])] TJ ET 0.271 0.267 0.267 rg BT 447.304 629.024 Td /F1 9.8 Tf [( . With additional purchases, )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(the Federal stockpile now remains at approximately 50 million treatment courses, but there is no clear quantitative guidance to )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(indicate the optimal use of these countermeasures.)] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(Key policy statements have called for the use of mathematical models to support the development of an evidence-based policy )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(for e?ectively deploying the remaining antiviral stockpile and other limited or costly measures to limit morbidity and mortality )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(from H1N1 )] TJ ET 0.267 0.267 0.267 rg BT 76.092 562.000 Td /F1 9.8 Tf [([2])] TJ ET BT 86.934 562.000 Td /F1 9.8 Tf [([3])] TJ ET 0.271 0.267 0.267 rg BT 97.776 562.000 Td /F1 9.8 Tf [( . While mathematical modelers have taken great strides towards building predictive models of disease )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(transmission dynamics within human populations, the computational complexity of these models often precludes systematic )] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(optimization of the demographic, spatial and temporal distribution of costly resources. Thus the typical approach has been to )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(evaluate a relatively small set of candidate strategies )] TJ ET 0.267 0.267 0.267 rg BT 257.101 526.286 Td /F1 9.8 Tf [([4])] TJ ET BT 267.943 526.286 Td /F1 9.8 Tf [([5])] TJ ET BT 278.785 526.286 Td /F1 9.8 Tf [([6])] TJ ET BT 289.627 526.286 Td /F1 9.8 Tf [([7])] TJ ET 0.271 0.267 0.267 rg BT 300.469 526.286 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 506.881 Td /F1 9.8 Tf [(Here, we use a new algorithm that efficiently searches large strategy spaces to analyze the optimal use of the U.S. antiviral )] TJ ET BT 26.250 494.976 Td /F1 9.8 Tf [(stockpile against pandemic influenza prior to widespread and effective vaccination. We assume, in line with CDC guidance, that )] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(antivirals will be used exclusively for treatment of symptomatic individuals rather than wide scale pre-exposure prophylaxis. We )] TJ ET BT 26.250 471.167 Td /F1 9.8 Tf [(apply our algorithm to a U.S. national-scale network model of H1N1 transmission that is based on demographic and travel data )] TJ ET BT 26.250 459.262 Td /F1 9.8 Tf [(from the U.S. Census Bureau and the Bureau of Transportation Statistics and assumes disease parameters estimated for H1N1 )] TJ ET BT 26.250 447.357 Td /F1 9.8 Tf [(during the initial March-April 2009 outbreak in Mexico City.)] TJ ET BT 26.250 410.755 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 390.801 Td /F1 9.8 Tf [(We couple a fast, scalable, and adaptable optimization algorithm to a detailed simulation model of influenza transmission within )] TJ ET BT 26.250 378.896 Td /F1 9.8 Tf [(and among the 100 largest cities in the United States. In brief, the method involves running many stochastic simulations of )] TJ ET BT 26.250 366.991 Td /F1 9.8 Tf [(H1N1 transmission, each requiring an intervention policy as an argument. The optimization algorithm dictates the choice of )] TJ ET BT 26.250 355.086 Td /F1 9.8 Tf [(intervention policy for each simulation, with the goal of identifying the optimal intervention policy given the highly stochastic )] TJ ET BT 26.250 343.182 Td /F1 9.8 Tf [(simulation output.)] TJ ET BT 26.250 306.579 Td /F4 12.0 Tf [(Optimization method)] TJ ET BT 26.250 285.349 Td /F1 9.8 Tf [(A time-based intervention policy is a series of actions )] TJ ET q 73.500 0 0 13.500 258.173 282.649 cm /I10 Do Q BT 331.673 285.349 Td /F1 9.8 Tf [( taken in sequence over )] TJ ET q 11.250 0 0 10.500 437.899 285.649 cm /I12 Do Q BT 449.149 285.349 Td /F1 9.8 Tf [( time periods \(Fig. 1\). Our )] TJ ET BT 26.250 273.125 Td /F1 9.8 Tf [(objective is to rapidly search large sets of time-based intervention policies to ?nd those that will be most e?ective at achieving a )] TJ ET BT 26.250 261.220 Td /F1 9.8 Tf [(public health goal, such as limiting morbidity and mortality associated with in?uenza. To achieve this, we use trees to represent )] TJ ET BT 26.250 249.315 Td /F1 9.8 Tf [(all possible policies \(Fig. 1\). The ?rst \(highest\) level of a policy tree is a single node attached to several edges; each of those )] TJ ET BT 26.250 237.411 Td /F1 9.8 Tf [(edges corresponds to one of the possible actions in the first time period and leads to a level-two node. Similarly each level-two )] TJ ET BT 26.250 225.506 Td /F1 9.8 Tf [(node is attached to edges corresponding to all possible actions during the second time period, and so on. Each intervention )] TJ ET BT 26.250 213.601 Td /F1 9.8 Tf [(policy corresponds to a unique path through the tree.)] TJ ET 0.965 0.965 0.965 rg 26.250 109.220 555.000 94.500 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 203.720 m 581.250 203.720 l 581.250 202.970 l 26.250 202.970 l f q 225.000 0 0 78.750 35.250 115.220 cm /I14 Do Q q 35.250 109.220 537.000 0.000 re W n Q Q q 15.000 109.220 577.500 667.780 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(In March/April 2009, a new swine-origin strain of influenza A/H1N1 virus emerged into human populations in California and )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(Mexico and has since escalated into a pandemic. The U.S. experienced low levels of sustained H1N1 transmission throughout )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(the summer months of 2009, and in the Southern hemisphere the novel virus largely displaced seasonal influenza, causing )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(more severe morbidity in a younger adults and children than is typical with the flu. Starting in September, the U.S. began to )] TJ ET BT 26.250 719.857 Td /F1 9.8 Tf [(experience large geo-temporally distinct outbreaks of influenza like illness and confirmed H1N1 disease in States and )] TJ ET BT 26.250 707.952 Td /F1 9.8 Tf [(Territories. As of mid-October, total cases reported by surveillance systems as well as pediatric deaths had surpassed levels )] TJ ET BT 26.250 696.048 Td /F1 9.8 Tf [(typically seen for the entire flu season ending in mid-Spring 2010.)] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(During the early weeks of the epidemic, the U.S. Centers for Disease Control and Prevention \(CDC\) distributed 11 million of the )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(50 million antiviral treatment courses from the federally held portion of the national antiviral stockpile. This distribution went to )] TJ ET BT 26.250 652.833 Td /F1 9.8 Tf [(States and Territories \(as well as to four large cities\) on a pro rata basis \(that is, in proportion to population size\). Since the )] TJ ET BT 26.250 640.929 Td /F1 9.8 Tf [(recipients had local stockpiles as well, this allowed the CDC to exceeded the pre-determined target of distribution of 31 million )] TJ ET BT 26.250 629.024 Td /F1 9.8 Tf [(treatment courses of oseltamivir and zanamivir prior to the acceleration phase of the pandemic )] TJ ET 0.267 0.267 0.267 rg BT 436.462 629.024 Td /F1 9.8 Tf [([1])] TJ ET 0.271 0.267 0.267 rg BT 447.304 629.024 Td /F1 9.8 Tf [( . With additional purchases, )] TJ ET BT 26.250 617.119 Td /F1 9.8 Tf [(the Federal stockpile now remains at approximately 50 million treatment courses, but there is no clear quantitative guidance to )] TJ ET BT 26.250 605.214 Td /F1 9.8 Tf [(indicate the optimal use of these countermeasures.)] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(Key policy statements have called for the use of mathematical models to support the development of an evidence-based policy )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(for e?ectively deploying the remaining antiviral stockpile and other limited or costly measures to limit morbidity and mortality )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(from H1N1 )] TJ ET 0.267 0.267 0.267 rg BT 76.092 562.000 Td /F1 9.8 Tf [([2])] TJ ET BT 86.934 562.000 Td /F1 9.8 Tf [([3])] TJ ET 0.271 0.267 0.267 rg BT 97.776 562.000 Td /F1 9.8 Tf [( . While mathematical modelers have taken great strides towards building predictive models of disease )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(transmission dynamics within human populations, the computational complexity of these models often precludes systematic )] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(optimization of the demographic, spatial and temporal distribution of costly resources. Thus the typical approach has been to )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(evaluate a relatively small set of candidate strategies )] TJ ET 0.267 0.267 0.267 rg BT 257.101 526.286 Td /F1 9.8 Tf [([4])] TJ ET BT 267.943 526.286 Td /F1 9.8 Tf [([5])] TJ ET BT 278.785 526.286 Td /F1 9.8 Tf [([6])] TJ ET BT 289.627 526.286 Td /F1 9.8 Tf [([7])] TJ ET 0.271 0.267 0.267 rg BT 300.469 526.286 Td /F1 9.8 Tf [( .)] TJ ET BT 26.250 506.881 Td /F1 9.8 Tf [(Here, we use a new algorithm that efficiently searches large strategy spaces to analyze the optimal use of the U.S. antiviral )] TJ ET BT 26.250 494.976 Td /F1 9.8 Tf [(stockpile against pandemic influenza prior to widespread and effective vaccination. We assume, in line with CDC guidance, that )] TJ ET BT 26.250 483.072 Td /F1 9.8 Tf [(antivirals will be used exclusively for treatment of symptomatic individuals rather than wide scale pre-exposure prophylaxis. We )] TJ ET BT 26.250 471.167 Td /F1 9.8 Tf [(apply our algorithm to a U.S. national-scale network model of H1N1 transmission that is based on demographic and travel data )] TJ ET BT 26.250 459.262 Td /F1 9.8 Tf [(from the U.S. Census Bureau and the Bureau of Transportation Statistics and assumes disease parameters estimated for H1N1 )] TJ ET BT 26.250 447.357 Td /F1 9.8 Tf [(during the initial March-April 2009 outbreak in Mexico City.)] TJ ET BT 26.250 410.755 Td /F4 12.0 Tf [(Methods)] TJ ET BT 26.250 390.801 Td /F1 9.8 Tf [(We couple a fast, scalable, and adaptable optimization algorithm to a detailed simulation model of influenza transmission within )] TJ ET BT 26.250 378.896 Td /F1 9.8 Tf [(and among the 100 largest cities in the United States. In brief, the method involves running many stochastic simulations of )] TJ ET BT 26.250 366.991 Td /F1 9.8 Tf [(H1N1 transmission, each requiring an intervention policy as an argument. The optimization algorithm dictates the choice of )] TJ ET BT 26.250 355.086 Td /F1 9.8 Tf [(intervention policy for each simulation, with the goal of identifying the optimal intervention policy given the highly stochastic )] TJ ET BT 26.250 343.182 Td /F1 9.8 Tf [(simulation output.)] TJ ET BT 26.250 306.579 Td /F4 12.0 Tf [(Optimization method)] TJ ET BT 26.250 285.349 Td /F1 9.8 Tf [(A time-based intervention policy is a series of actions )] TJ ET q 73.500 0 0 13.500 258.173 282.649 cm /I16 Do Q BT 331.673 285.349 Td /F1 9.8 Tf [( taken in sequence over )] TJ ET q 11.250 0 0 10.500 437.899 285.649 cm /I18 Do Q BT 449.149 285.349 Td /F1 9.8 Tf [( time periods \(Fig. 1\). Our )] TJ ET BT 26.250 273.125 Td /F1 9.8 Tf [(objective is to rapidly search large sets of time-based intervention policies to ?nd those that will be most e?ective at achieving a )] TJ ET BT 26.250 261.220 Td /F1 9.8 Tf [(public health goal, such as limiting morbidity and mortality associated with in?uenza. To achieve this, we use trees to represent )] TJ ET BT 26.250 249.315 Td /F1 9.8 Tf [(all possible policies \(Fig. 1\). The ?rst \(highest\) level of a policy tree is a single node attached to several edges; each of those )] TJ ET BT 26.250 237.411 Td /F1 9.8 Tf [(edges corresponds to one of the possible actions in the first time period and leads to a level-two node. Similarly each level-two )] TJ ET BT 26.250 225.506 Td /F1 9.8 Tf [(node is attached to edges corresponding to all possible actions during the second time period, and so on. Each intervention )] TJ ET BT 26.250 213.601 Td /F1 9.8 Tf [(policy corresponds to a unique path through the tree.)] TJ ET 0.965 0.965 0.965 rg 26.250 109.220 555.000 94.500 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 203.720 m 581.250 203.720 l 581.250 202.970 l 26.250 202.970 l f q 225.000 0 0 78.750 35.250 115.220 cm /I20 Do Q q 35.250 109.220 537.000 0.000 re W n Q Q q 225.000 0 0 78.750 35.250 115.220 cm /I22 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(2)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 58 0 obj << /Type /Annot /Subtype /Link /A 59 0 R /Border [0 0 0] /H /I /Rect [ 436.4617 628.1221 447.3037 638.0427 ] >> endobj 59 0 obj << /Type /Action >> endobj 60 0 obj << /Type /Annot /Subtype /Link /A 61 0 R /Border [0 0 0] /H /I /Rect [ 76.0920 561.0983 86.9340 571.0189 ] >> endobj 61 0 obj << /Type /Action >> endobj 62 0 obj << /Type /Annot /Subtype /Link /A 63 0 R /Border [0 0 0] /H /I /Rect [ 86.9340 561.0983 97.7760 571.0189 ] >> endobj 63 0 obj << /Type /Action >> endobj 64 0 obj << /Type /Annot /Subtype /Link /A 65 0 R /Border [0 0 0] /H /I /Rect [ 257.1008 525.3841 267.9427 535.3047 ] >> endobj 65 0 obj << /Type /Action >> endobj 66 0 obj << /Type /Annot /Subtype /Link /A 67 0 R /Border [0 0 0] /H /I /Rect [ 267.9428 525.3841 278.7848 535.3047 ] >> endobj 67 0 obj << /Type /Action >> endobj 68 0 obj << /Type /Annot /Subtype /Link /A 69 0 R /Border [0 0 0] /H /I /Rect [ 278.7848 525.3841 289.6268 535.3047 ] >> endobj 69 0 obj << /Type /Action >> endobj 70 0 obj << /Type /Annot /Subtype /Link /A 71 0 R /Border [0 0 0] /H /I /Rect [ 289.6268 525.3841 300.4688 535.3047 ] >> endobj 71 0 obj << /Type /Action >> endobj 72 0 obj << /Type /XObject /Subtype /Image /Width 98 /Height 18 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 98 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 611>> stream 8"a#Jde$sINNZ+d$묓N$III?$+YIx{ޙZ;yϼygx1 j W#|x4˜/~ph;lpT.%lfȟN/q|aB7XV&D&D/Ofy2R tVBi.) 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N7ȇEӑ-xҤRLԤIK ȲHM*Z*22e>̻^egόHTR(n!')Bf4MIP_ =d+S}F#zuM!WP奥l H:scծT%(+>E (  x! $,TTVVVŕ:CUN<'*6.3- DQ:rq*/p TZTD;tV 򧄇Sa :'JBV)jU*Օɕ66 ̇bscr5BJ2ϑ6 8tR봐 ]]NNt+lGxE| &B4tdэ*0Y2Xɹo`ٚfTrmØ\QJMN ʷ0b- N4Ɔk\Ce 0:=`0 lOXPii3cXEo__Z_?N\\;Y͇bvV+W\YĨs+ʱ c̞'{fSV@Yc @O̳ 8F( ܜ㘕7k43M0qB[ѽ KJ $k1%ZY|f&'͚;ӫ٩I|(*\^RBe 2ȇjm~U%e>Oߑc5DFd;õA)~1FCGLVW7wz mf ܙG@c쬄DCH8;Xώ2|9}lN+2!ǩRWX N !1s&%i^}? +/o&PVpjrRL,PT戮zcVT$@iEy|uX_MRϬR!!en0=|{Elo\e$ZzxN'aDgq0B5'SWKӐׂgWP]QZX&f<@PLN,tw;8:&M-DOOyzN*Q}bjB3nL@VckgGGR'heWwFNTzטi"ϐh4ֶ64 ljlc:%{dDц)L ̋> (e\]3|?_Tw\^c;JJD Y8X*"̘ W`*+'^M=I+ _ffe3e}Ii RTP ԭ--%C=;-9UW[8VI8LMz>Մ.U:@YBJ BSIY Y*Ա3f x55<f d,W _,_|(T|SRI2uL*eNFV^@NVVDTo3cgs,>s2eP^ M调CՏ 2rsæ3W/R4MMFZj՚43@a&\8b6Fy)̇Zi3ҩN|f-y( +a $V0}bErʋŔO];N^΅SǏ}kAbfsGGxy_^*'mnjspp_?o/1ti[@ҝE]ؤ0_-WJz1Ϳ1%)1CT*9}[G~g.B~nnFjQS@O'ƀJ;+zѿ'.}Nljhspxݷ~ C{rӧhC;o3?3dY%%{樣:,"IeV$3~M/l6g&['8?}d TZQZw'GhniA]ص}[OS'|mJZw@`YIJ1~e Nnv{w\bL&+),j҂Ύ'_{G3ǎ[!C§''S)A_ 2|`bB+ fy\ܽ|+$IFj;Ė4R/?nvQX;{]۷yegf1 zw?{[bT*H)ee5""\̹1nnlaBqy 0juV2ѩ R'L\kkk1ݮ ?1.+) DM =}*++\ମggdL ݝrW"uuwj㜬,q'LL о9WUT+_&puؿ Ĺ#Hs+[[)FRw b M&SG[/e29,d2]*-~ uf- &xʴp'fnPי:/=*++k+V3`4;:'L؄bGDϠE4~|Cmd>c88:XCOg` Bhz|q)'LP[k2TVV0}TSY1=rBV! jF%`|q-L5%}LRF,!Z )B(>av]U`/;8 *=4ř:={gwPsNh:Zgϙ3obWU^̦ /7ww/OGI$6aSTyyjNjڛΛG >avei <څ$*:RiB&&[;;s\]rJ[_]{{:ۖ\I=#Jˋ Ɇ_q>N5!!C!{{ 'V=Yj9-"uђ0}K%^9b+KKѸjpus򬩬 xǯ<1k_ewIh^?k֢ˮ4G\|Uy6yy\ܼk*}}|=D*>^6B'u-[Nl0<쳮n{o%cl[MNRXʜ#CԐSF1|g©L23|Q$ +XٸdV[%ou _ĠFxgO-dNLIQᨣ,VM"e_n9 >!>ׄr[% na&,MCZ"Xxdo$֑LQzТ'"E4GبQ(ܖ2F2_>r |-.':( !ʹCT˝ #7ugK+RVF61: ~ǚn2ɴyŴ[t2FWb$@FpjaV3rtQTyVCMLbvPf`qneԐߢ4+&FC?$ p,&x -"iUء8#IpfBU) W=Eq0tȒb$'S|$!Rn$s3$x?=ls endstream endobj 126 0 obj << /Type /Page /Parent 3 0 R /Annots [ 128 0 R 130 0 R 174 0 R 176 0 R 220 0 R 222 0 R ] /Contents 127 0 R >> endobj 127 0 obj << /Length 21617 >> stream q 15.000 34.738 577.500 742.262 re W n 0.965 0.965 0.965 rg 26.250 689.569 555.000 87.431 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 689.569 m 581.250 689.569 l 581.250 690.319 l 26.250 690.319 l f q 35.250 700.819 537.000 76.181 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 1.)] TJ ET BT 75.888 766.011 Td /F1 9.8 Tf [( Simply policy tree: Suppose there are three possible actions and, in each time step, we can only choose one of )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(them. Each level in the tree corresponds to a time step and branches represent possible actions. The red path through the )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(tree represents the following three-step time-based intervention: First choose action 3, then action 1, and finally action 3 )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(again. The policy tree for antiviral distribution has a similar organization. The UCT algorithm iteratively selects paths through )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(the tree that represent intervention policies to be simulated.)] TJ ET Q BT 26.250 672.545 Td /F1 9.8 Tf [(The naive approach to finding the optimal path through the tree is to simulate multiple disease outbreaks for each intervention )] TJ ET BT 26.250 660.640 Td /F1 9.8 Tf [(policy \(path\) and record the expected morbidity or mortality \(or other public health outcome measure\). However, such )] TJ ET BT 26.250 648.735 Td /F1 9.8 Tf [(exhaustive searches are computationally intractable for large trees. We can more efficiently search for the optimal policy by )] TJ ET BT 26.250 636.831 Td /F1 9.8 Tf [(prudently sampling paths from the tree.)] TJ ET BT 26.250 617.426 Td /F1 9.8 Tf [(To strategically search the tree, we use an optimization algorithm called Upper Confidence Bounds Applied to Trees \(UCT\) )] TJ ET 0.267 0.267 0.267 rg BT 557.830 617.426 Td /F1 9.8 Tf [([8])] TJ ET BT 568.672 617.426 Td /F1 9.8 Tf [([9])] TJ ET 0.271 0.267 0.267 rg BT 26.250 605.521 Td /F1 9.8 Tf [(. It selects paths from the tree using a multi-armed bandit algorithm inside of each tree node. The canonical application of a )] TJ ET BT 26.250 593.616 Td /F1 9.8 Tf [(bandit algorithm is maximizing the total payoff from playing a set of slot machines for a fixed number of rounds, where the payoff )] TJ ET BT 26.250 581.712 Td /F1 9.8 Tf [(distributions of the machines are unknown and, in each round, we may select only one machine. In this scenario, each edge )] TJ ET BT 26.250 569.807 Td /F1 9.8 Tf [(emanating from the node corresponds to a slot machine that can be chosen by the nodes bandit algorithm; for a policy tree, the )] TJ ET BT 26.250 557.902 Td /F1 9.8 Tf [(edges correspond to possible policy actions. Before each policy simulation, bandit algorithms within the nodes select an edge to )] TJ ET BT 26.250 545.997 Td /F1 9.8 Tf [(follow based on the results of prior trials. The combined choices of the bandit algorithms produce a path through the tree, )] TJ ET BT 26.250 534.093 Td /F1 9.8 Tf [(corresponding to a sequence of public health actions, that is then passed into the simulation. The bandit algorithms determine )] TJ ET BT 26.250 522.188 Td /F1 9.8 Tf [(which edge \(action\) to follow next by balancing two desirable characteristics: strong past performance and few prior trials. With )] TJ ET BT 26.250 510.283 Td /F1 9.8 Tf [(this strategic pathsampling, subtrees with good performance are explored more thoroughly than those with poor performance.)] TJ ET BT 26.250 490.878 Td /F1 9.8 Tf [(Specifically, suppose we are descending through the tree and have arrived at node )] TJ ET q 8.250 0 0 7.500 386.649 492.902 cm /I24 Do Q BT 394.899 490.878 Td /F1 9.8 Tf [(having )] TJ ET q 7.500 0 0 10.500 426.333 489.902 cm /I26 Do Q BT 433.833 490.878 Td /F1 9.8 Tf [( edges to the next level down, )] TJ ET q 69.000 0 0 15.000 26.250 473.497 cm /I28 Do Q BT 95.250 476.497 Td /F1 9.8 Tf [(, representing all possible subsequent actions. Let )] TJ ET q 31.500 0 0 15.000 314.196 473.497 cm /I30 Do Q BT 345.696 476.497 Td /F1 9.8 Tf [( be the number of times we have used the )] TJ ET BT 26.250 461.497 Td /F1 9.8 Tf [(intervention represented by edge )] TJ ET q 10.500 0 0 11.250 171.496 462.247 cm /I32 Do Q BT 181.996 461.497 Td /F1 9.8 Tf [( in prior simulations and )] TJ ET q 30.000 0 0 15.000 287.656 458.497 cm /I34 Do Q BT 317.656 461.497 Td /F1 9.8 Tf [( be a real number between 0 and 1, describing the average )] TJ ET BT 26.250 448.974 Td /F1 9.8 Tf [(rewards observed during past simulations where ei was chosen. In the analysis described below, the reward for a simulation is )] TJ ET BT 26.250 430.993 Td /F1 9.8 Tf [(the fraction of individuals that remain uninfected during the outbreak. Now define )] TJ ET q 90.000 0 0 19.500 376.343 427.093 cm /I36 Do Q BT 466.343 430.993 Td /F1 9.8 Tf [( to be the total number of )] TJ ET BT 26.250 417.569 Td /F1 9.8 Tf [(times we have used descendants of )] TJ ET q 8.250 0 0 7.500 183.956 419.593 cm /I38 Do Q BT 192.206 417.569 Td /F1 9.8 Tf [(in past simulations. We then select the next edge as given by)] TJ ET q 145.500 0 0 37.500 26.250 370.188 cm /I40 Do Q BT 171.750 377.688 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 351.288 Td /F1 9.8 Tf [(Initially,)] TJ ET q 27.000 0 0 14.250 58.757 348.438 cm /I42 Do Q BT 85.757 351.288 Td /F1 9.8 Tf [( and )] TJ ET q 25.500 0 0 14.250 107.441 348.438 cm /I44 Do Q BT 132.940 351.288 Td /F1 9.8 Tf [( are set to zero for each edge )] TJ ET q 6.000 0 0 7.500 263.015 355.188 cm /I46 Do Q BT 269.015 351.288 Td /F1 9.8 Tf [(. The first )] TJ ET q 7.500 0 0 10.500 312.364 352.188 cm /I48 Do Q BT 319.864 351.288 Td /F1 9.8 Tf [( times we arrive at node )] TJ ET q 8.250 0 0 7.500 426.070 355.188 cm /I50 Do Q BT 434.320 351.288 Td /F1 9.8 Tf [(, we choose the next edge )] TJ ET BT 26.250 338.914 Td /F1 9.8 Tf [(uniformly randomly from the previously unsampled edges descending from the node, rather than choosing an edge based on )] TJ ET BT 26.250 325.133 Td /F1 9.8 Tf [(the given equation. This gives initial estimates of )] TJ ET q 25.500 0 0 14.250 238.137 322.283 cm /I52 Do Q BT 263.637 325.133 Td /F1 9.8 Tf [( for each edge and guarantees that the equation is well defined. At the )] TJ ET BT 26.250 310.883 Td /F1 9.8 Tf [(end of each simulation run, if the simulation results in a reward of )] TJ ET q 7.500 0 0 10.500 309.663 311.783 cm /I54 Do Q BT 317.163 310.883 Td /F1 9.8 Tf [(, we update )] TJ ET q 27.000 0 0 14.250 370.281 308.033 cm /I56 Do Q BT 397.281 310.883 Td /F1 9.8 Tf [( and )] TJ ET q 25.500 0 0 14.250 418.965 308.033 cm /I58 Do Q BT 444.465 310.883 Td /F1 9.8 Tf [( for each edge )] TJ ET q 6.000 0 0 7.500 509.507 314.783 cm /I60 Do Q BT 515.507 310.883 Td /F1 9.8 Tf [( in the chosen )] TJ ET BT 26.250 298.509 Td /F1 9.8 Tf [(policy path, as given by)] TJ ET q 113.250 0 0 32.250 26.250 256.378 cm /I62 Do Q BT 139.500 262.828 Td /F1 9.8 Tf [(,)] TJ ET q 90.000 0 0 14.250 26.250 234.628 cm /I64 Do Q BT 116.250 237.478 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 200.407 Td /F4 12.0 Tf [(H1N1 transmission model)] TJ ET Q q 15.000 34.738 577.500 742.262 re W n 0.965 0.965 0.965 rg 26.250 689.569 555.000 87.431 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 689.569 m 581.250 689.569 l 581.250 690.319 l 26.250 690.319 l f q 35.250 700.819 537.000 76.181 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 1.)] TJ ET BT 75.888 766.011 Td /F1 9.8 Tf [( Simply policy tree: Suppose there are three possible actions and, in each time step, we can only choose one of )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(them. Each level in the tree corresponds to a time step and branches represent possible actions. The red path through the )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(tree represents the following three-step time-based intervention: First choose action 3, then action 1, and finally action 3 )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(again. The policy tree for antiviral distribution has a similar organization. The UCT algorithm iteratively selects paths through )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(the tree that represent intervention policies to be simulated.)] TJ ET Q BT 26.250 672.545 Td /F1 9.8 Tf [(The naive approach to finding the optimal path through the tree is to simulate multiple disease outbreaks for each intervention )] TJ ET BT 26.250 660.640 Td /F1 9.8 Tf [(policy \(path\) and record the expected morbidity or mortality \(or other public health outcome measure\). However, such )] TJ ET BT 26.250 648.735 Td /F1 9.8 Tf [(exhaustive searches are computationally intractable for large trees. We can more efficiently search for the optimal policy by )] TJ ET BT 26.250 636.831 Td /F1 9.8 Tf [(prudently sampling paths from the tree.)] TJ ET BT 26.250 617.426 Td /F1 9.8 Tf [(To strategically search the tree, we use an optimization algorithm called Upper Confidence Bounds Applied to Trees \(UCT\) )] TJ ET 0.267 0.267 0.267 rg BT 557.830 617.426 Td /F1 9.8 Tf [([8])] TJ ET BT 568.672 617.426 Td /F1 9.8 Tf [([9])] TJ ET 0.271 0.267 0.267 rg BT 26.250 605.521 Td /F1 9.8 Tf [(. It selects paths from the tree using a multi-armed bandit algorithm inside of each tree node. The canonical application of a )] TJ ET BT 26.250 593.616 Td /F1 9.8 Tf [(bandit algorithm is maximizing the total payoff from playing a set of slot machines for a fixed number of rounds, where the payoff )] TJ ET BT 26.250 581.712 Td /F1 9.8 Tf [(distributions of the machines are unknown and, in each round, we may select only one machine. In this scenario, each edge )] TJ ET BT 26.250 569.807 Td /F1 9.8 Tf [(emanating from the node corresponds to a slot machine that can be chosen by the nodes bandit algorithm; for a policy tree, the )] TJ ET BT 26.250 557.902 Td /F1 9.8 Tf [(edges correspond to possible policy actions. Before each policy simulation, bandit algorithms within the nodes select an edge to )] TJ ET BT 26.250 545.997 Td /F1 9.8 Tf [(follow based on the results of prior trials. The combined choices of the bandit algorithms produce a path through the tree, )] TJ ET BT 26.250 534.093 Td /F1 9.8 Tf [(corresponding to a sequence of public health actions, that is then passed into the simulation. The bandit algorithms determine )] TJ ET BT 26.250 522.188 Td /F1 9.8 Tf [(which edge \(action\) to follow next by balancing two desirable characteristics: strong past performance and few prior trials. With )] TJ ET BT 26.250 510.283 Td /F1 9.8 Tf [(this strategic pathsampling, subtrees with good performance are explored more thoroughly than those with poor performance.)] TJ ET BT 26.250 490.878 Td /F1 9.8 Tf [(Specifically, suppose we are descending through the tree and have arrived at node )] TJ ET q 8.250 0 0 7.500 386.649 492.902 cm /I66 Do Q BT 394.899 490.878 Td /F1 9.8 Tf [(having )] TJ ET q 7.500 0 0 10.500 426.333 489.902 cm /I68 Do Q BT 433.833 490.878 Td /F1 9.8 Tf [( edges to the next level down, )] TJ ET q 69.000 0 0 15.000 26.250 473.497 cm /I70 Do Q BT 95.250 476.497 Td /F1 9.8 Tf [(, representing all possible subsequent actions. Let )] TJ ET q 31.500 0 0 15.000 314.196 473.497 cm /I72 Do Q BT 345.696 476.497 Td /F1 9.8 Tf [( be the number of times we have used the )] TJ ET BT 26.250 461.497 Td /F1 9.8 Tf [(intervention represented by edge )] TJ ET q 10.500 0 0 11.250 171.496 462.247 cm /I74 Do Q BT 181.996 461.497 Td /F1 9.8 Tf [( in prior simulations and )] TJ ET q 30.000 0 0 15.000 287.656 458.497 cm /I76 Do Q BT 317.656 461.497 Td /F1 9.8 Tf [( be a real number between 0 and 1, describing the average )] TJ ET BT 26.250 448.974 Td /F1 9.8 Tf [(rewards observed during past simulations where ei was chosen. In the analysis described below, the reward for a simulation is )] TJ ET BT 26.250 430.993 Td /F1 9.8 Tf [(the fraction of individuals that remain uninfected during the outbreak. Now define )] TJ ET q 90.000 0 0 19.500 376.343 427.093 cm /I78 Do Q BT 466.343 430.993 Td /F1 9.8 Tf [( to be the total number of )] TJ ET BT 26.250 417.569 Td /F1 9.8 Tf [(times we have used descendants of )] TJ ET q 8.250 0 0 7.500 183.956 419.593 cm /I80 Do Q BT 192.206 417.569 Td /F1 9.8 Tf [(in past simulations. We then select the next edge as given by)] TJ ET q 145.500 0 0 37.500 26.250 370.188 cm /I82 Do Q BT 171.750 377.688 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 351.288 Td /F1 9.8 Tf [(Initially,)] TJ ET q 27.000 0 0 14.250 58.757 348.438 cm /I84 Do Q BT 85.757 351.288 Td /F1 9.8 Tf [( and )] TJ ET q 25.500 0 0 14.250 107.441 348.438 cm /I86 Do Q BT 132.940 351.288 Td /F1 9.8 Tf [( are set to zero for each edge )] TJ ET q 6.000 0 0 7.500 263.015 355.188 cm /I88 Do Q BT 269.015 351.288 Td /F1 9.8 Tf [(. The first )] TJ ET q 7.500 0 0 10.500 312.364 352.188 cm /I90 Do Q BT 319.864 351.288 Td /F1 9.8 Tf [( times we arrive at node )] TJ ET q 8.250 0 0 7.500 426.070 355.188 cm /I92 Do Q BT 434.320 351.288 Td /F1 9.8 Tf [(, we choose the next edge )] TJ ET BT 26.250 338.914 Td /F1 9.8 Tf [(uniformly randomly from the previously unsampled edges descending from the node, rather than choosing an edge based on )] TJ ET BT 26.250 325.133 Td /F1 9.8 Tf [(the given equation. This gives initial estimates of )] TJ ET q 25.500 0 0 14.250 238.137 322.283 cm /I94 Do Q BT 263.637 325.133 Td /F1 9.8 Tf [( for each edge and guarantees that the equation is well defined. At the )] TJ ET BT 26.250 310.883 Td /F1 9.8 Tf [(end of each simulation run, if the simulation results in a reward of )] TJ ET q 7.500 0 0 10.500 309.663 311.783 cm /I96 Do Q BT 317.163 310.883 Td /F1 9.8 Tf [(, we update )] TJ ET q 27.000 0 0 14.250 370.281 308.033 cm /I98 Do Q BT 397.281 310.883 Td /F1 9.8 Tf [( and )] TJ ET q 25.500 0 0 14.250 418.965 308.033 cm /I100 Do Q BT 444.465 310.883 Td /F1 9.8 Tf [( for each edge )] TJ ET q 6.000 0 0 7.500 509.507 314.783 cm /I102 Do Q BT 515.507 310.883 Td /F1 9.8 Tf [( in the chosen )] TJ ET BT 26.250 298.509 Td /F1 9.8 Tf [(policy path, as given by)] TJ ET q 113.250 0 0 32.250 26.250 256.378 cm /I104 Do Q BT 139.500 262.828 Td /F1 9.8 Tf [(,)] TJ ET q 90.000 0 0 14.250 26.250 234.628 cm /I106 Do Q BT 116.250 237.478 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 200.407 Td /F4 12.0 Tf [(H1N1 transmission model)] TJ ET Q q 15.000 34.738 577.500 742.262 re W n 0.965 0.965 0.965 rg 26.250 689.569 555.000 87.431 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 689.569 m 581.250 689.569 l 581.250 690.319 l 26.250 690.319 l f q 35.250 700.819 537.000 76.181 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 1.)] TJ ET BT 75.888 766.011 Td /F1 9.8 Tf [( Simply policy tree: Suppose there are three possible actions and, in each time step, we can only choose one of )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(them. Each level in the tree corresponds to a time step and branches represent possible actions. The red path through the )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(tree represents the following three-step time-based intervention: First choose action 3, then action 1, and finally action 3 )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(again. The policy tree for antiviral distribution has a similar organization. The UCT algorithm iteratively selects paths through )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(the tree that represent intervention policies to be simulated.)] TJ ET Q BT 26.250 672.545 Td /F1 9.8 Tf [(The naive approach to finding the optimal path through the tree is to simulate multiple disease outbreaks for each intervention )] TJ ET BT 26.250 660.640 Td /F1 9.8 Tf [(policy \(path\) and record the expected morbidity or mortality \(or other public health outcome measure\). However, such )] TJ ET BT 26.250 648.735 Td /F1 9.8 Tf [(exhaustive searches are computationally intractable for large trees. We can more efficiently search for the optimal policy by )] TJ ET BT 26.250 636.831 Td /F1 9.8 Tf [(prudently sampling paths from the tree.)] TJ ET BT 26.250 617.426 Td /F1 9.8 Tf [(To strategically search the tree, we use an optimization algorithm called Upper Confidence Bounds Applied to Trees \(UCT\) )] TJ ET 0.267 0.267 0.267 rg BT 557.830 617.426 Td /F1 9.8 Tf [([8])] TJ ET BT 568.672 617.426 Td /F1 9.8 Tf [([9])] TJ ET 0.271 0.267 0.267 rg BT 26.250 605.521 Td /F1 9.8 Tf [(. It selects paths from the tree using a multi-armed bandit algorithm inside of each tree node. The canonical application of a )] TJ ET BT 26.250 593.616 Td /F1 9.8 Tf [(bandit algorithm is maximizing the total payoff from playing a set of slot machines for a fixed number of rounds, where the payoff )] TJ ET BT 26.250 581.712 Td /F1 9.8 Tf [(distributions of the machines are unknown and, in each round, we may select only one machine. In this scenario, each edge )] TJ ET BT 26.250 569.807 Td /F1 9.8 Tf [(emanating from the node corresponds to a slot machine that can be chosen by the nodes bandit algorithm; for a policy tree, the )] TJ ET BT 26.250 557.902 Td /F1 9.8 Tf [(edges correspond to possible policy actions. Before each policy simulation, bandit algorithms within the nodes select an edge to )] TJ ET BT 26.250 545.997 Td /F1 9.8 Tf [(follow based on the results of prior trials. The combined choices of the bandit algorithms produce a path through the tree, )] TJ ET BT 26.250 534.093 Td /F1 9.8 Tf [(corresponding to a sequence of public health actions, that is then passed into the simulation. The bandit algorithms determine )] TJ ET BT 26.250 522.188 Td /F1 9.8 Tf [(which edge \(action\) to follow next by balancing two desirable characteristics: strong past performance and few prior trials. With )] TJ ET BT 26.250 510.283 Td /F1 9.8 Tf [(this strategic pathsampling, subtrees with good performance are explored more thoroughly than those with poor performance.)] TJ ET BT 26.250 490.878 Td /F1 9.8 Tf [(Specifically, suppose we are descending through the tree and have arrived at node )] TJ ET q 8.250 0 0 7.500 386.649 492.902 cm /I108 Do Q BT 394.899 490.878 Td /F1 9.8 Tf [(having )] TJ ET q 7.500 0 0 10.500 426.333 489.902 cm /I110 Do Q BT 433.833 490.878 Td /F1 9.8 Tf [( edges to the next level down, )] TJ ET q 69.000 0 0 15.000 26.250 473.497 cm /I112 Do Q BT 95.250 476.497 Td /F1 9.8 Tf [(, representing all possible subsequent actions. Let )] TJ ET q 31.500 0 0 15.000 314.196 473.497 cm /I114 Do Q BT 345.696 476.497 Td /F1 9.8 Tf [( be the number of times we have used the )] TJ ET BT 26.250 461.497 Td /F1 9.8 Tf [(intervention represented by edge )] TJ ET q 10.500 0 0 11.250 171.496 462.247 cm /I116 Do Q BT 181.996 461.497 Td /F1 9.8 Tf [( in prior simulations and )] TJ ET q 30.000 0 0 15.000 287.656 458.497 cm /I118 Do Q BT 317.656 461.497 Td /F1 9.8 Tf [( be a real number between 0 and 1, describing the average )] TJ ET BT 26.250 448.974 Td /F1 9.8 Tf [(rewards observed during past simulations where ei was chosen. In the analysis described below, the reward for a simulation is )] TJ ET BT 26.250 430.993 Td /F1 9.8 Tf [(the fraction of individuals that remain uninfected during the outbreak. Now define )] TJ ET q 90.000 0 0 19.500 376.343 427.093 cm /I120 Do Q BT 466.343 430.993 Td /F1 9.8 Tf [( to be the total number of )] TJ ET BT 26.250 417.569 Td /F1 9.8 Tf [(times we have used descendants of )] TJ ET q 8.250 0 0 7.500 183.956 419.593 cm /I122 Do Q BT 192.206 417.569 Td /F1 9.8 Tf [(in past simulations. We then select the next edge as given by)] TJ ET q 145.500 0 0 37.500 26.250 370.188 cm /I124 Do Q BT 171.750 377.688 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 351.288 Td /F1 9.8 Tf [(Initially,)] TJ ET q 27.000 0 0 14.250 58.757 348.438 cm /I126 Do Q BT 85.757 351.288 Td /F1 9.8 Tf [( and )] TJ ET q 25.500 0 0 14.250 107.441 348.438 cm /I128 Do Q BT 132.940 351.288 Td /F1 9.8 Tf [( are set to zero for each edge )] TJ ET q 6.000 0 0 7.500 263.015 355.188 cm /I130 Do Q BT 269.015 351.288 Td /F1 9.8 Tf [(. The first )] TJ ET q 7.500 0 0 10.500 312.364 352.188 cm /I132 Do Q BT 319.864 351.288 Td /F1 9.8 Tf [( times we arrive at node )] TJ ET q 8.250 0 0 7.500 426.070 355.188 cm /I134 Do Q BT 434.320 351.288 Td /F1 9.8 Tf [(, we choose the next edge )] TJ ET BT 26.250 338.914 Td /F1 9.8 Tf [(uniformly randomly from the previously unsampled edges descending from the node, rather than choosing an edge based on )] TJ ET BT 26.250 325.133 Td /F1 9.8 Tf [(the given equation. This gives initial estimates of )] TJ ET q 25.500 0 0 14.250 238.137 322.283 cm /I136 Do Q BT 263.637 325.133 Td /F1 9.8 Tf [( for each edge and guarantees that the equation is well defined. At the )] TJ ET BT 26.250 310.883 Td /F1 9.8 Tf [(end of each simulation run, if the simulation results in a reward of )] TJ ET q 7.500 0 0 10.500 309.663 311.783 cm /I138 Do Q BT 317.163 310.883 Td /F1 9.8 Tf [(, we update )] TJ ET q 27.000 0 0 14.250 370.281 308.033 cm /I140 Do Q BT 397.281 310.883 Td /F1 9.8 Tf [( and )] TJ ET q 25.500 0 0 14.250 418.965 308.033 cm /I142 Do Q BT 444.465 310.883 Td /F1 9.8 Tf [( for each edge )] TJ ET q 6.000 0 0 7.500 509.507 314.783 cm /I144 Do Q BT 515.507 310.883 Td /F1 9.8 Tf [( in the chosen )] TJ ET BT 26.250 298.509 Td /F1 9.8 Tf [(policy path, as given by)] TJ ET q 113.250 0 0 32.250 26.250 256.378 cm /I146 Do Q BT 139.500 262.828 Td /F1 9.8 Tf [(,)] TJ ET q 90.000 0 0 14.250 26.250 234.628 cm /I148 Do Q BT 116.250 237.478 Td /F1 9.8 Tf [(.)] TJ ET BT 26.250 200.407 Td /F4 12.0 Tf [(H1N1 transmission model)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(3)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 128 0 obj << /Type /Annot /Subtype /Link /A 129 0 R /Border [0 0 0] /H /I /Rect [ 557.8297 616.5241 568.6717 626.4447 ] >> endobj 129 0 obj << /Type /Action >> endobj 130 0 obj << /Type /Annot /Subtype /Link /A 131 0 R /Border [0 0 0] /H /I /Rect [ 568.6717 616.5241 579.5137 626.4447 ] >> endobj 131 0 obj << /Type /Action >> endobj 132 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 108>> stream c``ba`ay;j&0أ+ (&rHH)sz v 0H(a`8vΠĂP|Մ<4+M endstream endobj 133 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /SMask 132 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 13>> stream c`T endstream endobj 134 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 109>> stream c````aL0i0ϩ4SԄ aCY1e: f^@C J=aG C X)v(Y6kB! 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I@pȼssՃhԔ z1iagNb"$؟`7Y-K:껨]@¢Xѷ@AH?˼ Y}5؝U !d q ,֠]V5`VE p&<=a V endstream endobj 197 0 obj << /Type /XObject /Subtype /Image /Width 36 /Height 19 /SMask 196 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 36 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 24>> stream H  endstream endobj 198 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 329>> stream (c`,pLH &r}, cm"WHELHJ: 4ϩ) j9 %(΁; wS@\^V2̤ =2`%{;$wC(Y\;B3@Aq 0 6 SӀޅy AY 9`5,~%`+&1p-8cEBp[Ӓח.`']-34tZu%`#Y ,*t@o] endstream endobj 199 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /SMask 198 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 23>> stream 8c``Q0 F endstream endobj 200 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 83>> stream c`6c0cÄ#< |m0͍A\ QV kF &tuhey8G endstream endobj 201 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /SMask 200 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 12>> stream c` endstream endobj 202 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 109>> stream c````aL0i0ϩ4SԄ aCY1e: f^@C J=aG C X)v(Y6kB! \@ r endstream endobj 203 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /SMask 202 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 14>> stream c`C  endstream endobj 204 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 108>> stream c``ba`ay;j&0أ+ (&rHH)sz v 0H(a`8vΠĂP|Մ<4+M endstream endobj 205 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /SMask 204 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 13>> stream c`T endstream endobj 206 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 329>> stream (c`,pLH &r}, cm"WHELHJ: 4ϩ) j9 %(΁; wS@\^V2̤ =2`%{;$wC(Y\;B3@Aq 0 6 SӀޅy AY 9`5,~%`+&1p-8cEBp[Ӓח.`']-34tZu%`#Y ,*t@o] endstream endobj 207 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /SMask 206 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 23>> stream 8c``Q0 F endstream endobj 208 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 105>> stream c`.. 3o$&KnӁs$ k0`v Ĭ8+Vc\ 9 G|J2րX@naJXwd9~ endstream endobj 209 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /SMask 208 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 14>> stream c`C  endstream endobj 210 0 obj << /Type /XObject /Subtype /Image /Width 36 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 36 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 346>> stream (c`L-&&4W$aH4l8j Ye; DR븐14Ah=tIU>=`0d霛`;$Yy`Ka1 HՌi`V B.08YbFbv0YAz&-ٷ$ll! I@pȼssՃhԔ z1iagNb"$؟`7Y-K:껨]@¢Xѷ@AH?˼ Y}5؝U !d q ,֠]V5`VE p&<=a V endstream endobj 211 0 obj << /Type /XObject /Subtype /Image /Width 36 /Height 19 /SMask 210 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 36 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 24>> stream H  endstream endobj 212 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 329>> stream (c`,pLH &r}, cm"WHELHJ: 4ϩ) j9 %(΁; wS@\^V2̤ =2`%{;$wC(Y\;B3@Aq 0 6 SӀޅy AY 9`5,~%`+&1p-8cEBp[Ӓח.`']-34tZu%`#Y ,*t@o] endstream endobj 213 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /SMask 212 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 23>> stream 8c``Q0 F endstream endobj 214 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 83>> stream c`6c0cÄ#< |m0͍A\ QV kF &tuhey8G endstream endobj 215 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /SMask 214 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 12>> stream c` endstream endobj 216 0 obj << /Type /XObject /Subtype /Image /Width 151 /Height 43 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 151 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 1502>> stream XXgj+d$ɓIL3y2?WRH*omDRD@^#k*ue`_ ɂ*bPiM _ϢewG>*$z&i%6`=t *p$z"c\mAav}A/=}/?i '/Pc;dUᚏqE?r\ V+Iz&Y1 ^1lBNaFop͗⹟WO jYb@^G7595ɡZv#=;w;Ѡv'Zo#yBe_ 4PyIWD5*{95ĸEI-xY1yj@V]Jcߏoy}o^\LTIH q%ĽF@\h4Wհ: KBA|c 2yHVPr'l'0u&(Y>u4򳶼C`(-(㲤F3A@k=hOŨO3XCWXk8W\R6TfB^}+p=sU93חCJ_\3|~4TTȫ4f[5/1xB6&z/4l* VHbv endstream endobj 217 0 obj << /Type /XObject /Subtype /Image /Width 151 /Height 43 /SMask 216 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 151 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 42>> stream x  Om7LB endstream endobj 218 0 obj << /Type /XObject /Subtype /Image /Width 120 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 120 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 755>> stream Hg#Qu*""NSũsԩSUu"Tթ~:QkEEDDT|'ݛy687{3[B=#[\ ~bG:ϓl_죺 2q̿uફx$(>40CI7z5P6)NB+]F[ϧȤ|Ni װ]7F\TcDrlEXjC*LBL7 wJDvT.ʿʚ7Waz0e8"F܀lb`X~ٛko٪`I $\5z "XWLɬ6͵!#bk]fc]A_W(z;t4|pvx1rJāQp{&},=u i`vvKi_J̇@8nrhE{)ޘ\o@ޔє6>e̯Suyކ٨=@/G endstream endobj 219 0 obj << /Type /XObject /Subtype /Image /Width 120 /Height 19 /SMask 218 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 120 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 30>> stream X1 Om  endstream endobj 220 0 obj << /Type /Annot /Subtype /Link /A 221 0 R /Border [0 0 0] /H /I /Rect [ 557.8297 616.5241 568.6717 626.4447 ] >> endobj 221 0 obj << /Type /Action >> endobj 222 0 obj << /Type /Annot /Subtype /Link /A 223 0 R /Border [0 0 0] /H /I /Rect [ 568.6717 616.5241 579.5137 626.4447 ] >> endobj 223 0 obj << /Type /Action >> endobj 224 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 108>> stream c``ba`ay;j&0أ+ (&rHH)sz v 0H(a`8vΠĂP|Մ<4+M endstream endobj 225 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /SMask 224 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 13>> stream c`T endstream endobj 226 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 109>> stream c````aL0i0ϩ4SԄ aCY1e: f^@C J=aG C X)v(Y6kB! 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I@pȼssՃhԔ z1iagNb"$؟`7Y-K:껨]@¢Xѷ@AH?˼ Y}5؝U !d q ,֠]V5`VE p&<=a V endstream endobj 243 0 obj << /Type /XObject /Subtype /Image /Width 36 /Height 19 /SMask 242 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 36 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 24>> stream H  endstream endobj 244 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 329>> stream (c`,pLH &r}, cm"WHELHJ: 4ϩ) j9 %(΁; wS@\^V2̤ =2`%{;$wC(Y\;B3@Aq 0 6 SӀޅy AY 9`5,~%`+&1p-8cEBp[Ӓח.`']-34tZu%`#Y ,*t@o] endstream endobj 245 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /SMask 244 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 23>> stream 8c``Q0 F endstream endobj 246 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 83>> stream c`6c0cÄ#< |m0͍A\ QV kF &tuhey8G endstream endobj 247 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /SMask 246 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 12>> stream c` endstream endobj 248 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 109>> stream c````aL0i0ϩ4SԄ aCY1e: f^@C J=aG C X)v(Y6kB! \@ r endstream endobj 249 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /SMask 248 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 14>> stream c`C  endstream endobj 250 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 108>> stream c``ba`ay;j&0أ+ (&rHH)sz v 0H(a`8vΠĂP|Մ<4+M endstream endobj 251 0 obj << /Type /XObject /Subtype /Image /Width 11 /Height 10 /SMask 250 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 11 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 13>> stream c`T endstream endobj 252 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 329>> stream (c`,pLH &r}, cm"WHELHJ: 4ϩ) j9 %(΁; wS@\^V2̤ =2`%{;$wC(Y\;B3@Aq 0 6 SӀޅy AY 9`5,~%`+&1p-8cEBp[Ӓח.`']-34tZu%`#Y ,*t@o] endstream endobj 253 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /SMask 252 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 23>> stream 8c``Q0 F endstream endobj 254 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 105>> stream c`.. 3o$&KnӁs$ k0`v Ĭ8+Vc\ 9 G|J2րX@naJXwd9~ endstream endobj 255 0 obj << /Type /XObject /Subtype /Image /Width 10 /Height 14 /SMask 254 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 10 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 14>> stream c`C  endstream endobj 256 0 obj << /Type /XObject /Subtype /Image /Width 36 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 36 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 346>> stream (c`L-&&4W$aH4l8j Ye; DR븐14Ah=tIU>=`0d霛`;$Yy`Ka1 HՌi`V B.08YbFbv0YAz&-ٷ$ll! I@pȼssՃhԔ z1iagNb"$؟`7Y-K:껨]@¢Xѷ@AH?˼ Y}5؝U !d q ,֠]V5`VE p&<=a V endstream endobj 257 0 obj << /Type /XObject /Subtype /Image /Width 36 /Height 19 /SMask 256 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 36 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 24>> stream H  endstream endobj 258 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 329>> stream (c`,pLH &r}, cm"WHELHJ: 4ϩ) j9 %(΁; wS@\^V2̤ =2`%{;$wC(Y\;B3@Aq 0 6 SӀޅy AY 9`5,~%`+&1p-8cEBp[Ӓח.`']-34tZu%`#Y ,*t@o] endstream endobj 259 0 obj << /Type /XObject /Subtype /Image /Width 34 /Height 19 /SMask 258 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 34 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 23>> stream 8c``Q0 F endstream endobj 260 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 83>> stream c`6c0cÄ#< |m0͍A\ QV kF &tuhey8G endstream endobj 261 0 obj << /Type /XObject /Subtype /Image /Width 8 /Height 10 /SMask 260 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 8 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 12>> stream c` endstream endobj 262 0 obj << /Type /XObject /Subtype /Image /Width 151 /Height 43 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 151 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 1502>> stream XXgj+d$ɓIL3y2?WRH*omDRD@^#k*ue`_ ɂ*bPiM _ϢewG>*$z&i%6`=t *p$z"c\mAav}A/=}/?i '/Pc;dUᚏqE?r\ V+Iz&Y1 ^1lBNaFop͗⹟WO jYb@^G7595ɡZv#=;w;Ѡv'Zo#yBe_ 4PyIWD5*{95ĸEI-xY1yj@V]Jcߏoy}o^\LTIH q%ĽF@\h4Wհ: KBA|c 2yHVPr'l'0u&(Y>u4򳶼C`(-(㲤F3A@k=hOŨO3XCWXk8W\R6TfB^}+p=sU93חCJ_\3|~4TTȫ4f[5/1xB6&z/4l* VHbv endstream endobj 263 0 obj << /Type /XObject /Subtype /Image /Width 151 /Height 43 /SMask 262 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 151 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 42>> stream x  Om7LB endstream endobj 264 0 obj << /Type /XObject /Subtype /Image /Width 120 /Height 19 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 120 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 755>> stream Hg#Qu*""NSũsԩSUu"Tթ~:QkEEDDT|'ݛy687{3[B=#[\ ~bG:ϓl_죺 2q̿uફx$(>40CI7z5P6)NB+]F[ϧȤ|Ni װ]7F\TcDrlEXjC*LBL7 wJDvT.ʿʚ7Waz0e8"F܀lb`X~ٛko٪`I $\5z "XWLɬ6͵!#bk]fc]A_W(z;t4|pvx1rJāQp{&},=u i`vvKi_J̇@8nrhE{)ޘ\o@ޔє6>e̯Suyކ٨=@/G endstream endobj 265 0 obj << /Type /XObject /Subtype /Image /Width 120 /Height 19 /SMask 264 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 120 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 30>> stream X1 Om  endstream endobj 266 0 obj << /Type /Page /Parent 3 0 R /Annots [ 268 0 R 270 0 R 272 0 R 274 0 R 280 0 R 300 0 R 302 0 R 306 0 R 308 0 R 310 0 R 312 0 R 314 0 R 316 0 R 318 0 R 324 0 R 330 0 R 332 0 R 334 0 R 336 0 R 338 0 R 344 0 R 364 0 R 366 0 R 370 0 R 372 0 R 374 0 R 376 0 R 378 0 R 380 0 R 382 0 R 388 0 R 394 0 R 396 0 R 398 0 R 400 0 R 402 0 R 408 0 R 428 0 R 430 0 R 434 0 R 436 0 R 438 0 R 440 0 R 442 0 R 444 0 R 446 0 R 452 0 R 458 0 R ] /Contents 267 0 R >> endobj 267 0 obj << /Length 28733 >> stream 0.271 0.267 0.267 rg q 15.000 31.771 577.500 745.229 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Our model includes the 100 largest metropolitan areas in the United States, which we identified by aggregating Census Bureau )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(Statistical Areas \(CBSA\) that share a common airport )] TJ ET 0.267 0.267 0.267 rg BT 259.246 755.571 Td /F1 9.8 Tf [([10])] TJ ET BT 275.509 755.571 Td /F1 9.8 Tf [([11])] TJ ET 0.271 0.267 0.267 rg BT 291.772 755.571 Td /F1 9.8 Tf [( . We model movement among cities using both Census Bureaus )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(County-To-County Worker Flow Files )] TJ ET 0.267 0.267 0.267 rg BT 189.319 743.667 Td /F1 9.8 Tf [([12])] TJ ET 0.271 0.267 0.267 rg BT 205.582 743.667 Td /F1 9.8 Tf [( and the Bureau of Transportation Statistics Origin and Destination Survey for all )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(quarters of 2007, which contains a 10 % sample of all itineraries between U.S. cities )] TJ ET 0.267 0.267 0.267 rg BT 390.949 731.762 Td /F1 9.8 Tf [([13])] TJ ET 0.271 0.267 0.267 rg BT 407.212 731.762 Td /F1 9.8 Tf [(. We assume that each latent traveler )] TJ ET BT 26.250 708.381 Td /F1 9.8 Tf [(to a city has some chance of sparking an epidemic and that the probability of this happening is )] TJ ET q 46.500 0 0 26.250 435.418 703.131 cm /I150 Do Q BT 481.918 708.381 Td /F1 9.8 Tf [(, where )] TJ ET q 9.000 0 0 11.250 516.599 718.131 cm /I152 Do Q BT 525.599 708.381 Td /F1 9.8 Tf [( is the )] TJ ET BT 26.250 693.607 Td /F1 9.8 Tf [(fraction of susceptible individuals in the destination citys population, as holds for a simple stochastic SIR model )] TJ ET 0.267 0.267 0.267 rg BT 509.080 693.607 Td /F1 9.8 Tf [([14])] TJ ET 0.271 0.267 0.267 rg BT 525.343 693.607 Td /F1 9.8 Tf [(. If there are )] TJ ET q 12.000 0 0 10.500 26.250 680.726 cm /I154 Do Q BT 38.250 681.702 Td /F1 9.8 Tf [( infected travelers this week from city )] TJ ET q 10.500 0 0 11.250 200.802 679.976 cm /I156 Do Q BT 211.302 681.702 Td /F1 9.8 Tf [( to city )] TJ ET q 10.500 0 0 10.500 242.190 680.726 cm /I158 Do Q BT 252.690 681.702 Td /F1 9.8 Tf [( and the fraction of susceptibles in city )] TJ ET q 10.500 0 0 10.500 420.146 680.726 cm /I160 Do Q BT 430.646 681.702 Td /F1 9.8 Tf [( is )] TJ ET q 9.000 0 0 11.250 443.107 679.976 cm /I162 Do Q BT 452.107 681.702 Td /F1 9.8 Tf [(, then the model draws a )] TJ ET BT 26.250 658.322 Td /F1 9.8 Tf [(binomial random variable from the distribution )] TJ ET q 123.750 0 0 26.250 226.193 653.072 cm /I164 Do Q BT 349.943 658.322 Td /F1 9.8 Tf [( and creates that many new infected individuals in )] TJ ET BT 26.250 643.548 Td /F1 9.8 Tf [(city )] TJ ET q 10.500 0 0 10.500 43.585 642.572 cm /I166 Do Q BT 54.085 643.548 Td /F1 9.8 Tf [(. The number of infected travelers from city )] TJ ET q 10.500 0 0 11.250 242.114 641.822 cm /I168 Do Q BT 252.614 643.548 Td /F1 9.8 Tf [( to city )] TJ ET q 10.500 0 0 10.500 283.502 642.572 cm /I170 Do Q BT 294.002 643.548 Td /F1 9.8 Tf [( is calculated based on the travel data given as input, under the )] TJ ET BT 26.250 631.643 Td /F1 9.8 Tf [(assumptions that symptomatic individuals do not travel and travelers are selected uniformly randomly from the population.)] TJ ET BT 26.250 612.238 Td /F1 9.8 Tf [(Within each city, disease transmission is modeled using a compartmental model with five compartments: susceptible, exposed, )] TJ ET BT 26.250 600.333 Td /F1 9.8 Tf [(asymptomatic infectious, symptomatic infectious, and recovered \(Fig. 2b\). Progression from one compartment to another is )] TJ ET BT 26.250 588.429 Td /F1 9.8 Tf [(governed by published estimates for H1N1 transmission and disease progression rates, as given in Table 1. Epidemics are )] TJ ET BT 26.250 576.524 Td /F1 9.8 Tf [(initialized assuming that there are 100,000 cases of H1N1 in the United States \(corresponding to the late June CDC estimate of )] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(over one million H1N1 cases )] TJ ET 0.267 0.267 0.267 rg BT 153.039 564.619 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 169.302 564.619 Td /F1 9.8 Tf [( \) distributed stochastically, proportional to city sizes. Assuming conservatively that universal )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(H1N1 vaccine coverage will be achieved within 12 months, we terminate the simulations after 12 months or when all cases have )] TJ ET BT 26.250 540.810 Td /F1 9.8 Tf [(recovered, whichever occurs first.)] TJ ET 0.965 0.965 0.965 rg 26.250 387.720 555.000 143.209 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 530.929 m 581.250 530.929 l 581.250 530.179 l 26.250 530.179 l f 26.250 387.720 m 581.250 387.720 l 581.250 388.470 l 26.250 388.470 l f q 225.000 0 0 67.500 35.250 453.679 cm /I172 Do Q q 35.250 398.970 537.000 48.709 re W n 0.271 0.267 0.267 rg BT 35.250 436.690 Td /F4 9.8 Tf [(Table 1.)] TJ ET BT 71.559 436.690 Td /F1 9.8 Tf [( H1N1 transmission and intervention parameters. References: reproductive number )] TJ ET 0.267 0.267 0.267 rg BT 433.528 436.690 Td /F1 9.8 Tf [([16])] TJ ET BT 449.791 436.690 Td /F1 9.8 Tf [([17])] TJ ET 0.271 0.267 0.267 rg BT 466.054 436.690 Td /F1 9.8 Tf [( ; average latency )] TJ ET BT 35.250 422.953 Td /F1 9.8 Tf [(period )] TJ ET 0.267 0.267 0.267 rg BT 65.056 422.953 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 81.319 422.953 Td /F1 9.8 Tf [( ; average asymptomatic infectious period )] TJ ET 0.267 0.267 0.267 rg BT 263.936 422.953 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 280.199 422.953 Td /F1 9.8 Tf [( ; average total infectious period \(asymptomatic + symptomatic\) )] TJ ET 0.267 0.267 0.267 rg BT 35.250 409.217 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 51.513 409.217 Td /F1 9.8 Tf [( ; antiviral efficacy )] TJ ET 0.267 0.267 0.267 rg BT 131.707 409.217 Td /F1 9.8 Tf [([19][20][21][22][23][24][25])] TJ ET 0.271 0.267 0.267 rg BT 245.548 409.217 Td /F1 9.8 Tf [(.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 183.566 555.000 196.654 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 380.220 m 581.250 380.220 l 581.250 379.470 l 26.250 379.470 l f 26.250 183.566 m 581.250 183.566 l 581.250 184.316 l 26.250 184.316 l f q 225.000 0 0 66.000 35.250 304.470 cm /I174 Do Q q 35.250 194.816 537.000 103.654 re W n 0.271 0.267 0.267 rg BT 35.250 287.481 Td /F4 9.8 Tf [(Figure 2.)] TJ ET BT 75.888 287.481 Td /F1 9.8 Tf [( Disease Model. \(2a\) The U.S. network model for influenza transmission. Circle sizes represent numbers of )] TJ ET BT 35.250 273.745 Td /F1 9.8 Tf [(inhabitants and line thickness represents the number of travelers between cities. \(2b\) Within-city compartmental model. )] TJ ET BT 35.250 260.008 Td /F1 9.8 Tf [(When infected individuals progress from asymptomatic to symptomatic they seek treatment at a rate U \(uptake\) and receive )] TJ ET BT 35.250 246.272 Td /F1 9.8 Tf [(treatment if antiviral courses are available locally. While disease transmission is a continuous process, antivirals are )] TJ ET BT 35.250 232.536 Td /F1 9.8 Tf [(distributed once per day to those requiring treatment. Antivirals are assumed to be 80 % effective; and effectively treated )] TJ ET BT 35.250 218.800 Td /F1 9.8 Tf [(cases immediately move to the recovered compartment. Untreated and ineffectively treated cases remain infectious until )] TJ ET BT 35.250 205.063 Td /F1 9.8 Tf [(they recover naturally. The parameters of the compartmental model are described in Table 1.)] TJ ET Q BT 26.250 149.345 Td /F4 12.0 Tf [(Antiviral policy actions)] TJ ET BT 26.250 129.390 Td /F1 9.8 Tf [(The model considers 11 possible antiviral stockpile actions every month over a twelve month period: distribution of 0, 1, 5, 10, )] TJ ET BT 26.250 117.486 Td /F1 9.8 Tf [(25 or 50 million courses apportioned either pro rata or proportional to current prevalence. We assume that, post distribution, )] TJ ET BT 26.250 105.581 Td /F1 9.8 Tf [(unused courses decay through misuse or loss at a rate )] TJ ET q 15.000 0 0 11.250 265.778 103.855 cm /I176 Do Q BT 280.778 105.581 Td /F1 9.8 Tf [(. Clinically, we assume that antivirals are 80 % efficacious at )] TJ ET BT 26.250 93.676 Td /F1 9.8 Tf [(reducing disease and infectiousness )] TJ ET 0.267 0.267 0.267 rg BT 186.121 93.676 Td /F1 9.8 Tf [([19][20][21][22][23][24][25])] TJ ET 0.271 0.267 0.267 rg BT 299.962 93.676 Td /F1 9.8 Tf [(. If an infected individual resides in a jurisdiction with remaining )] TJ ET BT 26.250 81.771 Td /F1 9.8 Tf [(distributed antivirals, then they receive appropriate treatment \(i. e., access to medications within 24 hours of onset of symptoms\) )] TJ ET BT 26.250 69.867 Td /F1 9.8 Tf [(with an uptake probability of )] TJ ET q 10.500 0 0 11.250 149.812 68.140 cm /I178 Do Q BT 160.312 69.867 Td /F1 9.8 Tf [(. Effectively treated infected cases \(i. e., )] TJ ET q 45.000 0 0 11.250 335.354 68.140 cm /I180 Do Q BT 380.354 69.867 Td /F1 9.8 Tf [(\) are immediately moved from the infectious )] TJ ET BT 26.250 57.962 Td /F1 9.8 Tf [(to the recovered compartment, consistent with early evidence of rapid decline in viral titers in treated H1N1 patients )] TJ ET 0.267 0.267 0.267 rg BT 525.333 57.962 Td /F1 9.8 Tf [([26])] TJ ET 0.271 0.267 0.267 rg BT 541.596 57.962 Td /F1 9.8 Tf [(. )] TJ ET BT 26.250 46.057 Td /F1 9.8 Tf [(Consistent with current CDC antiviral guidance, we did not model the use of antivirals for large scale prophylaxis of susceptible )] TJ ET Q q 15.000 31.771 577.500 745.229 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Our model includes the 100 largest metropolitan areas in the United States, which we identified by aggregating Census Bureau )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(Statistical Areas \(CBSA\) that share a common airport )] TJ ET 0.267 0.267 0.267 rg BT 259.246 755.571 Td /F1 9.8 Tf [([10])] TJ ET BT 275.509 755.571 Td /F1 9.8 Tf [([11])] TJ ET 0.271 0.267 0.267 rg BT 291.772 755.571 Td /F1 9.8 Tf [( . We model movement among cities using both Census Bureaus )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(County-To-County Worker Flow Files )] TJ ET 0.267 0.267 0.267 rg BT 189.319 743.667 Td /F1 9.8 Tf [([12])] TJ ET 0.271 0.267 0.267 rg BT 205.582 743.667 Td /F1 9.8 Tf [( and the Bureau of Transportation Statistics Origin and Destination Survey for all )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(quarters of 2007, which contains a 10 % sample of all itineraries between U.S. cities )] TJ ET 0.267 0.267 0.267 rg BT 390.949 731.762 Td /F1 9.8 Tf [([13])] TJ ET 0.271 0.267 0.267 rg BT 407.212 731.762 Td /F1 9.8 Tf [(. We assume that each latent traveler )] TJ ET BT 26.250 708.381 Td /F1 9.8 Tf [(to a city has some chance of sparking an epidemic and that the probability of this happening is )] TJ ET q 46.500 0 0 26.250 435.418 703.131 cm /I182 Do Q BT 481.918 708.381 Td /F1 9.8 Tf [(, where )] TJ ET q 9.000 0 0 11.250 516.599 718.131 cm /I184 Do Q BT 525.599 708.381 Td /F1 9.8 Tf [( is the )] TJ ET BT 26.250 693.607 Td /F1 9.8 Tf [(fraction of susceptible individuals in the destination citys population, as holds for a simple stochastic SIR model )] TJ ET 0.267 0.267 0.267 rg BT 509.080 693.607 Td /F1 9.8 Tf [([14])] TJ ET 0.271 0.267 0.267 rg BT 525.343 693.607 Td /F1 9.8 Tf [(. If there are )] TJ ET q 12.000 0 0 10.500 26.250 680.726 cm /I186 Do Q BT 38.250 681.702 Td /F1 9.8 Tf [( infected travelers this week from city )] TJ ET q 10.500 0 0 11.250 200.802 679.976 cm /I188 Do Q BT 211.302 681.702 Td /F1 9.8 Tf [( to city )] TJ ET q 10.500 0 0 10.500 242.190 680.726 cm /I190 Do Q BT 252.690 681.702 Td /F1 9.8 Tf [( and the fraction of susceptibles in city )] TJ ET q 10.500 0 0 10.500 420.146 680.726 cm /I192 Do Q BT 430.646 681.702 Td /F1 9.8 Tf [( is )] TJ ET q 9.000 0 0 11.250 443.107 679.976 cm /I194 Do Q BT 452.107 681.702 Td /F1 9.8 Tf [(, then the model draws a )] TJ ET BT 26.250 658.322 Td /F1 9.8 Tf [(binomial random variable from the distribution )] TJ ET q 123.750 0 0 26.250 226.193 653.072 cm /I196 Do Q BT 349.943 658.322 Td /F1 9.8 Tf [( and creates that many new infected individuals in )] TJ ET BT 26.250 643.548 Td /F1 9.8 Tf [(city )] TJ ET q 10.500 0 0 10.500 43.585 642.572 cm /I198 Do Q BT 54.085 643.548 Td /F1 9.8 Tf [(. The number of infected travelers from city )] TJ ET q 10.500 0 0 11.250 242.114 641.822 cm /I200 Do Q BT 252.614 643.548 Td /F1 9.8 Tf [( to city )] TJ ET q 10.500 0 0 10.500 283.502 642.572 cm /I202 Do Q BT 294.002 643.548 Td /F1 9.8 Tf [( is calculated based on the travel data given as input, under the )] TJ ET BT 26.250 631.643 Td /F1 9.8 Tf [(assumptions that symptomatic individuals do not travel and travelers are selected uniformly randomly from the population.)] TJ ET BT 26.250 612.238 Td /F1 9.8 Tf [(Within each city, disease transmission is modeled using a compartmental model with five compartments: susceptible, exposed, )] TJ ET BT 26.250 600.333 Td /F1 9.8 Tf [(asymptomatic infectious, symptomatic infectious, and recovered \(Fig. 2b\). Progression from one compartment to another is )] TJ ET BT 26.250 588.429 Td /F1 9.8 Tf [(governed by published estimates for H1N1 transmission and disease progression rates, as given in Table 1. Epidemics are )] TJ ET BT 26.250 576.524 Td /F1 9.8 Tf [(initialized assuming that there are 100,000 cases of H1N1 in the United States \(corresponding to the late June CDC estimate of )] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(over one million H1N1 cases )] TJ ET 0.267 0.267 0.267 rg BT 153.039 564.619 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 169.302 564.619 Td /F1 9.8 Tf [( \) distributed stochastically, proportional to city sizes. Assuming conservatively that universal )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(H1N1 vaccine coverage will be achieved within 12 months, we terminate the simulations after 12 months or when all cases have )] TJ ET BT 26.250 540.810 Td /F1 9.8 Tf [(recovered, whichever occurs first.)] TJ ET 0.965 0.965 0.965 rg 26.250 387.720 555.000 143.209 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 530.929 m 581.250 530.929 l 581.250 530.179 l 26.250 530.179 l f 26.250 387.720 m 581.250 387.720 l 581.250 388.470 l 26.250 388.470 l f q 225.000 0 0 67.500 35.250 453.679 cm /I204 Do Q q 35.250 398.970 537.000 48.709 re W n 0.271 0.267 0.267 rg BT 35.250 436.690 Td /F4 9.8 Tf [(Table 1.)] TJ ET BT 71.559 436.690 Td /F1 9.8 Tf [( H1N1 transmission and intervention parameters. References: reproductive number )] TJ ET 0.267 0.267 0.267 rg BT 433.528 436.690 Td /F1 9.8 Tf [([16])] TJ ET BT 449.791 436.690 Td /F1 9.8 Tf [([17])] TJ ET 0.271 0.267 0.267 rg BT 466.054 436.690 Td /F1 9.8 Tf [( ; average latency )] TJ ET BT 35.250 422.953 Td /F1 9.8 Tf [(period )] TJ ET 0.267 0.267 0.267 rg BT 65.056 422.953 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 81.319 422.953 Td /F1 9.8 Tf [( ; average asymptomatic infectious period )] TJ ET 0.267 0.267 0.267 rg BT 263.936 422.953 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 280.199 422.953 Td /F1 9.8 Tf [( ; average total infectious period \(asymptomatic + symptomatic\) )] TJ ET 0.267 0.267 0.267 rg BT 35.250 409.217 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 51.513 409.217 Td /F1 9.8 Tf [( ; antiviral efficacy )] TJ ET 0.267 0.267 0.267 rg BT 131.707 409.217 Td /F1 9.8 Tf [([19][20][21][22][23][24][25])] TJ ET 0.271 0.267 0.267 rg BT 245.548 409.217 Td /F1 9.8 Tf [(.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 183.566 555.000 196.654 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 380.220 m 581.250 380.220 l 581.250 379.470 l 26.250 379.470 l f 26.250 183.566 m 581.250 183.566 l 581.250 184.316 l 26.250 184.316 l f q 225.000 0 0 66.000 35.250 304.470 cm /I206 Do Q q 35.250 194.816 537.000 103.654 re W n 0.271 0.267 0.267 rg BT 35.250 287.481 Td /F4 9.8 Tf [(Figure 2.)] TJ ET BT 75.888 287.481 Td /F1 9.8 Tf [( Disease Model. \(2a\) The U.S. network model for influenza transmission. Circle sizes represent numbers of )] TJ ET BT 35.250 273.745 Td /F1 9.8 Tf [(inhabitants and line thickness represents the number of travelers between cities. \(2b\) Within-city compartmental model. )] TJ ET BT 35.250 260.008 Td /F1 9.8 Tf [(When infected individuals progress from asymptomatic to symptomatic they seek treatment at a rate U \(uptake\) and receive )] TJ ET BT 35.250 246.272 Td /F1 9.8 Tf [(treatment if antiviral courses are available locally. While disease transmission is a continuous process, antivirals are )] TJ ET BT 35.250 232.536 Td /F1 9.8 Tf [(distributed once per day to those requiring treatment. Antivirals are assumed to be 80 % effective; and effectively treated )] TJ ET BT 35.250 218.800 Td /F1 9.8 Tf [(cases immediately move to the recovered compartment. Untreated and ineffectively treated cases remain infectious until )] TJ ET BT 35.250 205.063 Td /F1 9.8 Tf [(they recover naturally. The parameters of the compartmental model are described in Table 1.)] TJ ET Q BT 26.250 149.345 Td /F4 12.0 Tf [(Antiviral policy actions)] TJ ET BT 26.250 129.390 Td /F1 9.8 Tf [(The model considers 11 possible antiviral stockpile actions every month over a twelve month period: distribution of 0, 1, 5, 10, )] TJ ET BT 26.250 117.486 Td /F1 9.8 Tf [(25 or 50 million courses apportioned either pro rata or proportional to current prevalence. We assume that, post distribution, )] TJ ET BT 26.250 105.581 Td /F1 9.8 Tf [(unused courses decay through misuse or loss at a rate )] TJ ET q 15.000 0 0 11.250 265.778 103.855 cm /I208 Do Q BT 280.778 105.581 Td /F1 9.8 Tf [(. Clinically, we assume that antivirals are 80 % efficacious at )] TJ ET BT 26.250 93.676 Td /F1 9.8 Tf [(reducing disease and infectiousness )] TJ ET 0.267 0.267 0.267 rg BT 186.121 93.676 Td /F1 9.8 Tf [([19][20][21][22][23][24][25])] TJ ET 0.271 0.267 0.267 rg BT 299.962 93.676 Td /F1 9.8 Tf [(. If an infected individual resides in a jurisdiction with remaining )] TJ ET BT 26.250 81.771 Td /F1 9.8 Tf [(distributed antivirals, then they receive appropriate treatment \(i. e., access to medications within 24 hours of onset of symptoms\) )] TJ ET BT 26.250 69.867 Td /F1 9.8 Tf [(with an uptake probability of )] TJ ET q 10.500 0 0 11.250 149.812 68.140 cm /I210 Do Q BT 160.312 69.867 Td /F1 9.8 Tf [(. Effectively treated infected cases \(i. e., )] TJ ET q 45.000 0 0 11.250 335.354 68.140 cm /I212 Do Q BT 380.354 69.867 Td /F1 9.8 Tf [(\) are immediately moved from the infectious )] TJ ET BT 26.250 57.962 Td /F1 9.8 Tf [(to the recovered compartment, consistent with early evidence of rapid decline in viral titers in treated H1N1 patients )] TJ ET 0.267 0.267 0.267 rg BT 525.333 57.962 Td /F1 9.8 Tf [([26])] TJ ET 0.271 0.267 0.267 rg BT 541.596 57.962 Td /F1 9.8 Tf [(. )] TJ ET BT 26.250 46.057 Td /F1 9.8 Tf [(Consistent with current CDC antiviral guidance, we did not model the use of antivirals for large scale prophylaxis of susceptible )] TJ ET Q q 15.000 31.771 577.500 745.229 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(Our model includes the 100 largest metropolitan areas in the United States, which we identified by aggregating Census Bureau )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(Statistical Areas \(CBSA\) that share a common airport )] TJ ET 0.267 0.267 0.267 rg BT 259.246 755.571 Td /F1 9.8 Tf [([10])] TJ ET BT 275.509 755.571 Td /F1 9.8 Tf [([11])] TJ ET 0.271 0.267 0.267 rg BT 291.772 755.571 Td /F1 9.8 Tf [( . We model movement among cities using both Census Bureaus )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(County-To-County Worker Flow Files )] TJ ET 0.267 0.267 0.267 rg BT 189.319 743.667 Td /F1 9.8 Tf [([12])] TJ ET 0.271 0.267 0.267 rg BT 205.582 743.667 Td /F1 9.8 Tf [( and the Bureau of Transportation Statistics Origin and Destination Survey for all )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(quarters of 2007, which contains a 10 % sample of all itineraries between U.S. cities )] TJ ET 0.267 0.267 0.267 rg BT 390.949 731.762 Td /F1 9.8 Tf [([13])] TJ ET 0.271 0.267 0.267 rg BT 407.212 731.762 Td /F1 9.8 Tf [(. We assume that each latent traveler )] TJ ET BT 26.250 708.381 Td /F1 9.8 Tf [(to a city has some chance of sparking an epidemic and that the probability of this happening is )] TJ ET q 46.500 0 0 26.250 435.418 703.131 cm /I214 Do Q BT 481.918 708.381 Td /F1 9.8 Tf [(, where )] TJ ET q 9.000 0 0 11.250 516.599 718.131 cm /I216 Do Q BT 525.599 708.381 Td /F1 9.8 Tf [( is the )] TJ ET BT 26.250 693.607 Td /F1 9.8 Tf [(fraction of susceptible individuals in the destination citys population, as holds for a simple stochastic SIR model )] TJ ET 0.267 0.267 0.267 rg BT 509.080 693.607 Td /F1 9.8 Tf [([14])] TJ ET 0.271 0.267 0.267 rg BT 525.343 693.607 Td /F1 9.8 Tf [(. If there are )] TJ ET q 12.000 0 0 10.500 26.250 680.726 cm /I218 Do Q BT 38.250 681.702 Td /F1 9.8 Tf [( infected travelers this week from city )] TJ ET q 10.500 0 0 11.250 200.802 679.976 cm /I220 Do Q BT 211.302 681.702 Td /F1 9.8 Tf [( to city )] TJ ET q 10.500 0 0 10.500 242.190 680.726 cm /I222 Do Q BT 252.690 681.702 Td /F1 9.8 Tf [( and the fraction of susceptibles in city )] TJ ET q 10.500 0 0 10.500 420.146 680.726 cm /I224 Do Q BT 430.646 681.702 Td /F1 9.8 Tf [( is )] TJ ET q 9.000 0 0 11.250 443.107 679.976 cm /I226 Do Q BT 452.107 681.702 Td /F1 9.8 Tf [(, then the model draws a )] TJ ET BT 26.250 658.322 Td /F1 9.8 Tf [(binomial random variable from the distribution )] TJ ET q 123.750 0 0 26.250 226.193 653.072 cm /I228 Do Q BT 349.943 658.322 Td /F1 9.8 Tf [( and creates that many new infected individuals in )] TJ ET BT 26.250 643.548 Td /F1 9.8 Tf [(city )] TJ ET q 10.500 0 0 10.500 43.585 642.572 cm /I230 Do Q BT 54.085 643.548 Td /F1 9.8 Tf [(. The number of infected travelers from city )] TJ ET q 10.500 0 0 11.250 242.114 641.822 cm /I232 Do Q BT 252.614 643.548 Td /F1 9.8 Tf [( to city )] TJ ET q 10.500 0 0 10.500 283.502 642.572 cm /I234 Do Q BT 294.002 643.548 Td /F1 9.8 Tf [( is calculated based on the travel data given as input, under the )] TJ ET BT 26.250 631.643 Td /F1 9.8 Tf [(assumptions that symptomatic individuals do not travel and travelers are selected uniformly randomly from the population.)] TJ ET BT 26.250 612.238 Td /F1 9.8 Tf [(Within each city, disease transmission is modeled using a compartmental model with five compartments: susceptible, exposed, )] TJ ET BT 26.250 600.333 Td /F1 9.8 Tf [(asymptomatic infectious, symptomatic infectious, and recovered \(Fig. 2b\). Progression from one compartment to another is )] TJ ET BT 26.250 588.429 Td /F1 9.8 Tf [(governed by published estimates for H1N1 transmission and disease progression rates, as given in Table 1. Epidemics are )] TJ ET BT 26.250 576.524 Td /F1 9.8 Tf [(initialized assuming that there are 100,000 cases of H1N1 in the United States \(corresponding to the late June CDC estimate of )] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(over one million H1N1 cases )] TJ ET 0.267 0.267 0.267 rg BT 153.039 564.619 Td /F1 9.8 Tf [([15])] TJ ET 0.271 0.267 0.267 rg BT 169.302 564.619 Td /F1 9.8 Tf [( \) distributed stochastically, proportional to city sizes. Assuming conservatively that universal )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(H1N1 vaccine coverage will be achieved within 12 months, we terminate the simulations after 12 months or when all cases have )] TJ ET BT 26.250 540.810 Td /F1 9.8 Tf [(recovered, whichever occurs first.)] TJ ET 0.965 0.965 0.965 rg 26.250 387.720 555.000 143.209 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 530.929 m 581.250 530.929 l 581.250 530.179 l 26.250 530.179 l f 26.250 387.720 m 581.250 387.720 l 581.250 388.470 l 26.250 388.470 l f q 225.000 0 0 67.500 35.250 453.679 cm /I236 Do Q q 35.250 398.970 537.000 48.709 re W n 0.271 0.267 0.267 rg BT 35.250 436.690 Td /F4 9.8 Tf [(Table 1.)] TJ ET BT 71.559 436.690 Td /F1 9.8 Tf [( H1N1 transmission and intervention parameters. References: reproductive number )] TJ ET 0.267 0.267 0.267 rg BT 433.528 436.690 Td /F1 9.8 Tf [([16])] TJ ET BT 449.791 436.690 Td /F1 9.8 Tf [([17])] TJ ET 0.271 0.267 0.267 rg BT 466.054 436.690 Td /F1 9.8 Tf [( ; average latency )] TJ ET BT 35.250 422.953 Td /F1 9.8 Tf [(period )] TJ ET 0.267 0.267 0.267 rg BT 65.056 422.953 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 81.319 422.953 Td /F1 9.8 Tf [( ; average asymptomatic infectious period )] TJ ET 0.267 0.267 0.267 rg BT 263.936 422.953 Td /F1 9.8 Tf [([16])] TJ ET 0.271 0.267 0.267 rg BT 280.199 422.953 Td /F1 9.8 Tf [( ; average total infectious period \(asymptomatic + symptomatic\) )] TJ ET 0.267 0.267 0.267 rg BT 35.250 409.217 Td /F1 9.8 Tf [([18])] TJ ET 0.271 0.267 0.267 rg BT 51.513 409.217 Td /F1 9.8 Tf [( ; antiviral efficacy )] TJ ET 0.267 0.267 0.267 rg BT 131.707 409.217 Td /F1 9.8 Tf [([19][20][21][22][23][24][25])] TJ ET 0.271 0.267 0.267 rg BT 245.548 409.217 Td /F1 9.8 Tf [(.)] TJ ET Q 0.965 0.965 0.965 rg 26.250 183.566 555.000 196.654 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 380.220 m 581.250 380.220 l 581.250 379.470 l 26.250 379.470 l f 26.250 183.566 m 581.250 183.566 l 581.250 184.316 l 26.250 184.316 l f q 225.000 0 0 66.000 35.250 304.470 cm /I238 Do Q q 35.250 194.816 537.000 103.654 re W n 0.271 0.267 0.267 rg BT 35.250 287.481 Td /F4 9.8 Tf [(Figure 2.)] TJ ET BT 75.888 287.481 Td /F1 9.8 Tf [( Disease Model. \(2a\) The U.S. network model for influenza transmission. Circle sizes represent numbers of )] TJ ET BT 35.250 273.745 Td /F1 9.8 Tf [(inhabitants and line thickness represents the number of travelers between cities. \(2b\) Within-city compartmental model. )] TJ ET BT 35.250 260.008 Td /F1 9.8 Tf [(When infected individuals progress from asymptomatic to symptomatic they seek treatment at a rate U \(uptake\) and receive )] TJ ET BT 35.250 246.272 Td /F1 9.8 Tf [(treatment if antiviral courses are available locally. While disease transmission is a continuous process, antivirals are )] TJ ET BT 35.250 232.536 Td /F1 9.8 Tf [(distributed once per day to those requiring treatment. Antivirals are assumed to be 80 % effective; and effectively treated )] TJ ET BT 35.250 218.800 Td /F1 9.8 Tf [(cases immediately move to the recovered compartment. Untreated and ineffectively treated cases remain infectious until )] TJ ET BT 35.250 205.063 Td /F1 9.8 Tf [(they recover naturally. The parameters of the compartmental model are described in Table 1.)] TJ ET Q BT 26.250 149.345 Td /F4 12.0 Tf [(Antiviral policy actions)] TJ ET BT 26.250 129.390 Td /F1 9.8 Tf [(The model considers 11 possible antiviral stockpile actions every month over a twelve month period: distribution of 0, 1, 5, 10, )] TJ ET BT 26.250 117.486 Td /F1 9.8 Tf [(25 or 50 million courses apportioned either pro rata or proportional to current prevalence. We assume that, post distribution, )] TJ ET BT 26.250 105.581 Td /F1 9.8 Tf [(unused courses decay through misuse or loss at a rate )] TJ ET q 15.000 0 0 11.250 265.778 103.855 cm /I240 Do Q BT 280.778 105.581 Td /F1 9.8 Tf [(. Clinically, we assume that antivirals are 80 % efficacious at )] TJ ET BT 26.250 93.676 Td /F1 9.8 Tf [(reducing disease and infectiousness )] TJ ET 0.267 0.267 0.267 rg BT 186.121 93.676 Td /F1 9.8 Tf [([19][20][21][22][23][24][25])] TJ ET 0.271 0.267 0.267 rg BT 299.962 93.676 Td /F1 9.8 Tf [(. If an infected individual resides in a jurisdiction with remaining )] TJ ET BT 26.250 81.771 Td /F1 9.8 Tf [(distributed antivirals, then they receive appropriate treatment \(i. e., access to medications within 24 hours of onset of symptoms\) )] TJ ET BT 26.250 69.867 Td /F1 9.8 Tf [(with an uptake probability of )] TJ ET q 10.500 0 0 11.250 149.812 68.140 cm /I242 Do Q BT 160.312 69.867 Td /F1 9.8 Tf [(. Effectively treated infected cases \(i. e., )] TJ ET q 45.000 0 0 11.250 335.354 68.140 cm /I244 Do Q BT 380.354 69.867 Td /F1 9.8 Tf [(\) are immediately moved from the infectious )] TJ ET BT 26.250 57.962 Td /F1 9.8 Tf [(to the recovered compartment, consistent with early evidence of rapid decline in viral titers in treated H1N1 patients )] TJ ET 0.267 0.267 0.267 rg BT 525.333 57.962 Td /F1 9.8 Tf [([26])] TJ ET 0.271 0.267 0.267 rg BT 541.596 57.962 Td /F1 9.8 Tf [(. )] TJ ET BT 26.250 46.057 Td /F1 9.8 Tf [(Consistent with current CDC antiviral guidance, we did not model the use of antivirals for large scale prophylaxis of susceptible )] TJ ET Q q 225.000 0 0 67.500 35.250 453.679 cm /I246 Do Q q 225.000 0 0 66.000 35.250 304.470 cm /I248 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(4)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 268 0 obj << /Type /Annot /Subtype /Link /A 269 0 R /Border [0 0 0] /H /I /Rect [ 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Ʀ*?rRG9ƕ$8vU\qˮ\A(GD 8k=i% v33'?nwOOwOdS[=w9]TJcR?qBSmnh흸ٓc?;<=^RةH=i^_u{T:35qbDB ڜs-a[% [m{"ӻW7eT,|>U$!M-ʸ/Z4>{n|r(A"+Z`$՞|^l (X>zz lЗȟ4MRkƘEM03aͨK!Á%9by#<wDxDTD N?ȎzG/BLvKDHi޾|TE:{ܒ>DTU'*p ~sȹh*E[2J'h:&@@`ɶmDA H?zwsƗSޖ˥PjiT&\X#85 H8O:qZ"Vp<4M"0~[on8~xWWWggi7 ѣ=Ν;{zz۳٬{ٰaCPڸqǗ-[688X(cYBr&s;LL uQ |or_ܷữ}7,ujE˶7Lvt PU*_GacT0 $cpS?yaljzҬ$H5.lhQ`RIbBhLu.-Ede3BXDNdSvrV"ww\54}{3 .%;zS/x˂^sZr&8l@6!C~ ׵׆0D FNg&C@XJInqvo-G%Or;vxǶmۖDwwȈ(˗/tM)Sw4n,s)u S 6e, }o=hi|dz6Lոp#YK8}W&XN4"c:B1QWO7fe#"A{$z^MMMsssoE6뮻N}ѱe˖N۶|:]X,ʓJ|5GT$<,Gvkru]1Dխ7,cV76utf-o- JKEde[LmUlLjin>ɫ@ƙ?280DBd 7!0"!l&l"bB%lYLՐ"W&&SdUz'=?O ë !y^}/*U5?M5*y۶;.@gr=0fZ V0">D"z:FD0;f͚6fB^D2<@˪Q I EstvQ/|0cDOw>z;ھu-ܞ"`Ur*l,[z~7 Hρ" ل Q~gðA(ZP]LJ["L놪#aݲZO[sd9%Ku]~0}zrziWo/ϰ.$\;/Kz5mMӴ_Z_O#w{G~0Ҏ>! 9;+}k2U3)L׏^)/Lqҧf@vljIO^/4v(!"ؤ*ٹY8ܰfy>(XW[`* ,$=]mO& Ɓ) hۆ{ʍ0;v_U_| UŬ5yQUWe{~d_MfŶ'^|w lZu%@T=!R[sKTtq]3EV)@|oLM5>iDgTǸ_T=M.Vbrê/# Ry(("Uœ4_|oXzW*FN3D!lhβbI T5Ue>~MC(q!y"""!|bq6ZʜMöED,\L/JskԚ?$Né !L+َHϱeKGV:m]3 sL k?g a~KPv|~ӶTK4$(z@:N~NO D뭯x{$e4=tapA7,X+jDYT4TMO[BSU+N-yU* ݻ+pGfӧ}mB+mqν~r@D3O[֖\>D"J)\$c'L ~J Fɮ]6o,98yaQmԥO<]:;;Ν;wy睟oEV,0ԨRՁddd0w}wbb ᡁc"9R(qDL&>5.*:a;wi75nZ(844t:thll'\.g]T5důQ޽{ʕ211 /\r˪3Z!IF>OZLDhٲeSSS\s(BA4 a9a\ T/zCoh_d``ҥͦi:ujpp0wmì7GR+ 0reYX$Zy4{G2:w޽{リLD Ԃ2p_S065o^Pcɲ[>^m۶=*UM|BqbQX躾[kJ}IvjJ!bzUjgE/0f9I5<~s3VB"3R&Ȃd5/Wՠb`eU Z0W1#DrU_Xs&Lߨm3ߜZ;f.e4:aé}3?|4RUUUH^? 12#`oRCU9,TaZd%YbdvT (URԢ endstream endobj 464 0 obj << /Type /Page /Parent 3 0 R /Annots [ 466 0 R 472 0 R 476 0 R 482 0 R 486 0 R 492 0 R ] /Contents 465 0 R >> endobj 465 0 obj << /Length 16234 >> stream 0.271 0.267 0.267 rg q 15.000 -96.371 577.500 873.371 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(populations in the absence of infection.)] TJ ET BT 26.250 730.874 Td /F4 12.0 Tf [(Computational requirements)] TJ ET BT 26.250 710.919 Td /F1 9.8 Tf [(Each optimization is based on 48 hours of computation on the Linux Lonestar Cluster at the Texas Advanced Computing )] TJ ET BT 26.250 699.015 Td /F1 9.8 Tf [(Center, which offers a peak performance of 10.7 GFLOPS per optimization process. Roughly 1,000,000 simulations can be )] TJ ET BT 26.250 687.110 Td /F1 9.8 Tf [(done in this time; however, for this relatively small action space, the optimal policy is typically identified within six hours of )] TJ ET BT 26.250 675.205 Td /F1 9.8 Tf [(computation.)] TJ ET BT 26.250 638.603 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 618.648 Td /F1 9.8 Tf [(Without antivirals, the expected cumulative number of cases after 12 months is almost 128 million. We found several optimized )] TJ ET BT 26.250 606.744 Td /F1 9.8 Tf [(time-based intervention policies that decrease the spread of disease. Figure 3a shows the comparison of these strategies with a )] TJ ET BT 26.250 594.839 Td /F1 9.8 Tf [(range of naive distribution policies in which fixed fractions of the antiviral stockpile are distributed monthly. Notably, one of these )] TJ ET BT 26.250 582.934 Td /F1 9.8 Tf [(naive policies monthly releases of 5 million regimens pro rata for 10 months consistently performs as well as the optimized )] TJ ET BT 26.250 571.029 Td /F1 9.8 Tf [(policies and better than other naive policies, particularly at uptake rates between 20 % and 60 %. Naive monthly distributions of )] TJ ET BT 26.250 559.125 Td /F1 9.8 Tf [(less than 5 million regimens fail to meet the demand while larger monthly distributions result in greater wastage and rapid )] TJ ET BT 26.250 547.220 Td /F1 9.8 Tf [(exhaustion of the stockpile \(Fig. 3b\).)] TJ ET 0.965 0.965 0.965 rg 26.250 239.713 555.000 297.626 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 537.339 m 581.250 537.339 l 581.250 536.589 l 26.250 536.589 l f 26.250 239.713 m 581.250 239.713 l 581.250 240.463 l 26.250 240.463 l f q 225.000 0 0 139.500 35.250 388.089 cm /I250 Do Q q 35.250 250.963 537.000 131.126 re W n 0.271 0.267 0.267 rg BT 35.250 371.100 Td /F4 9.8 Tf [(Figure 3.)] TJ ET BT 75.888 371.100 Td /F1 9.8 Tf [( Optimizer performance. \(3a\) The optimal policies perform at least as well as the naive strategies of distributing )] TJ ET BT 35.250 357.364 Td /F1 9.8 Tf [(fixed quantities each month until the stockpile is depleted. The four best policies are completely overlapping in the graph: )] TJ ET BT 35.250 343.627 Td /F1 9.8 Tf [(the optimal policy when there is no wastage, the optimal pro rata policy, the optimal policy combining both prevalence-)] TJ ET BT 35.250 329.891 Td /F1 9.8 Tf [(based and pro rata distributions, and the simple strategy of distributing 5M courses per month for ten months. In contrast, )] TJ ET BT 35.250 316.155 Td /F1 9.8 Tf [(the other simple strategies perform poorly for many uptake values. \(3b\) Predicted prevalence curves at an uptake of 50 %. )] TJ ET BT 35.250 302.419 Td /F1 9.8 Tf [(From top to bottom: without intervention, with the optimal intervention policy, releasing 1 million courses every month, )] TJ ET BT 35.250 288.682 Td /F1 9.8 Tf [(releasing 25 million courses in each of the first two months. The dashed lines represent the total number of antivirals )] TJ ET BT 35.250 274.946 Td /F1 9.8 Tf [(distributed and available for treatment. The 1 million per month policy does not release enough antivirals to meet demand; )] TJ ET BT 35.250 261.210 Td /F1 9.8 Tf [(and the 25 million policy leads to a rapid depletion of antivirals, followed by a spike in the number of infections.)] TJ ET Q BT 26.250 222.689 Td /F1 9.8 Tf [(The optimal policy returned by the algorithm is sensitive to the levels of uptake \()] TJ ET q 10.500 0 0 11.250 369.811 220.963 cm /I252 Do Q BT 380.311 222.689 Td /F1 9.8 Tf [(\), but, remarkably, the optimal policies under )] TJ ET BT 26.250 210.784 Td /F1 9.8 Tf [(high levels of wastage \(loss of half of unused supplies every two months\) are predicted to perform as well as optimal policies )] TJ ET BT 26.250 198.879 Td /F1 9.8 Tf [(under no wastage \(Fig. 3a\). Under perfect conditions of no loss or misallocation of antivirals, then there is no reason to reserve )] TJ ET BT 26.250 186.975 Td /F1 9.8 Tf [(the stockpile and the optimal strategies are always a series of large distributions early in the outbreak.)] TJ ET BT 26.250 167.570 Td /F1 9.8 Tf [(A mixed pro rata and prevalence-based distribution policy favored pro rata distributions, particularly for low to intermediate )] TJ ET BT 26.250 155.665 Td /F1 9.8 Tf [(levels of uptake \(Fig. 4a\). This combined with the comparable performance of exclusively pro rata policies \(Fig. 3a\) suggests )] TJ ET BT 26.250 143.760 Td /F1 9.8 Tf [(that prevalence-based distributions are probably unnecessary.)] TJ ET 0.965 0.965 0.965 rg 26.250 -96.371 555.000 230.250 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 133.879 m 581.250 133.879 l 581.250 133.129 l 26.250 133.129 l f q 225.000 0 0 214.500 35.250 -90.371 cm /I254 Do Q q 35.250 -96.371 537.000 0.000 re W n Q Q q 15.000 -96.371 577.500 873.371 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(populations in the absence of infection.)] TJ ET BT 26.250 730.874 Td /F4 12.0 Tf [(Computational requirements)] TJ ET BT 26.250 710.919 Td /F1 9.8 Tf [(Each optimization is based on 48 hours of computation on the Linux Lonestar Cluster at the Texas Advanced Computing )] TJ ET BT 26.250 699.015 Td /F1 9.8 Tf [(Center, which offers a peak performance of 10.7 GFLOPS per optimization process. Roughly 1,000,000 simulations can be )] TJ ET BT 26.250 687.110 Td /F1 9.8 Tf [(done in this time; however, for this relatively small action space, the optimal policy is typically identified within six hours of )] TJ ET BT 26.250 675.205 Td /F1 9.8 Tf [(computation.)] TJ ET BT 26.250 638.603 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 618.648 Td /F1 9.8 Tf [(Without antivirals, the expected cumulative number of cases after 12 months is almost 128 million. We found several optimized )] TJ ET BT 26.250 606.744 Td /F1 9.8 Tf [(time-based intervention policies that decrease the spread of disease. Figure 3a shows the comparison of these strategies with a )] TJ ET BT 26.250 594.839 Td /F1 9.8 Tf [(range of naive distribution policies in which fixed fractions of the antiviral stockpile are distributed monthly. Notably, one of these )] TJ ET BT 26.250 582.934 Td /F1 9.8 Tf [(naive policies monthly releases of 5 million regimens pro rata for 10 months consistently performs as well as the optimized )] TJ ET BT 26.250 571.029 Td /F1 9.8 Tf [(policies and better than other naive policies, particularly at uptake rates between 20 % and 60 %. Naive monthly distributions of )] TJ ET BT 26.250 559.125 Td /F1 9.8 Tf [(less than 5 million regimens fail to meet the demand while larger monthly distributions result in greater wastage and rapid )] TJ ET BT 26.250 547.220 Td /F1 9.8 Tf [(exhaustion of the stockpile \(Fig. 3b\).)] TJ ET 0.965 0.965 0.965 rg 26.250 239.713 555.000 297.626 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 537.339 m 581.250 537.339 l 581.250 536.589 l 26.250 536.589 l f 26.250 239.713 m 581.250 239.713 l 581.250 240.463 l 26.250 240.463 l f q 225.000 0 0 139.500 35.250 388.089 cm /I256 Do Q q 35.250 250.963 537.000 131.126 re W n 0.271 0.267 0.267 rg BT 35.250 371.100 Td /F4 9.8 Tf [(Figure 3.)] TJ ET BT 75.888 371.100 Td /F1 9.8 Tf [( Optimizer performance. \(3a\) The optimal policies perform at least as well as the naive strategies of distributing )] TJ ET BT 35.250 357.364 Td /F1 9.8 Tf [(fixed quantities each month until the stockpile is depleted. The four best policies are completely overlapping in the graph: )] TJ ET BT 35.250 343.627 Td /F1 9.8 Tf [(the optimal policy when there is no wastage, the optimal pro rata policy, the optimal policy combining both prevalence-)] TJ ET BT 35.250 329.891 Td /F1 9.8 Tf [(based and pro rata distributions, and the simple strategy of distributing 5M courses per month for ten months. In contrast, )] TJ ET BT 35.250 316.155 Td /F1 9.8 Tf [(the other simple strategies perform poorly for many uptake values. \(3b\) Predicted prevalence curves at an uptake of 50 %. )] TJ ET BT 35.250 302.419 Td /F1 9.8 Tf [(From top to bottom: without intervention, with the optimal intervention policy, releasing 1 million courses every month, )] TJ ET BT 35.250 288.682 Td /F1 9.8 Tf [(releasing 25 million courses in each of the first two months. The dashed lines represent the total number of antivirals )] TJ ET BT 35.250 274.946 Td /F1 9.8 Tf [(distributed and available for treatment. The 1 million per month policy does not release enough antivirals to meet demand; )] TJ ET BT 35.250 261.210 Td /F1 9.8 Tf [(and the 25 million policy leads to a rapid depletion of antivirals, followed by a spike in the number of infections.)] TJ ET Q BT 26.250 222.689 Td /F1 9.8 Tf [(The optimal policy returned by the algorithm is sensitive to the levels of uptake \()] TJ ET q 10.500 0 0 11.250 369.811 220.963 cm /I258 Do Q BT 380.311 222.689 Td /F1 9.8 Tf [(\), but, remarkably, the optimal policies under )] TJ ET BT 26.250 210.784 Td /F1 9.8 Tf [(high levels of wastage \(loss of half of unused supplies every two months\) are predicted to perform as well as optimal policies )] TJ ET BT 26.250 198.879 Td /F1 9.8 Tf [(under no wastage \(Fig. 3a\). Under perfect conditions of no loss or misallocation of antivirals, then there is no reason to reserve )] TJ ET BT 26.250 186.975 Td /F1 9.8 Tf [(the stockpile and the optimal strategies are always a series of large distributions early in the outbreak.)] TJ ET BT 26.250 167.570 Td /F1 9.8 Tf [(A mixed pro rata and prevalence-based distribution policy favored pro rata distributions, particularly for low to intermediate )] TJ ET BT 26.250 155.665 Td /F1 9.8 Tf [(levels of uptake \(Fig. 4a\). This combined with the comparable performance of exclusively pro rata policies \(Fig. 3a\) suggests )] TJ ET BT 26.250 143.760 Td /F1 9.8 Tf [(that prevalence-based distributions are probably unnecessary.)] TJ ET 0.965 0.965 0.965 rg 26.250 -96.371 555.000 230.250 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 133.879 m 581.250 133.879 l 581.250 133.129 l 26.250 133.129 l f q 225.000 0 0 214.500 35.250 -90.371 cm /I260 Do Q q 35.250 -96.371 537.000 0.000 re W n Q Q q 15.000 -96.371 577.500 873.371 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(populations in the absence of infection.)] TJ ET BT 26.250 730.874 Td /F4 12.0 Tf [(Computational requirements)] TJ ET BT 26.250 710.919 Td /F1 9.8 Tf [(Each optimization is based on 48 hours of computation on the Linux Lonestar Cluster at the Texas Advanced Computing )] TJ ET BT 26.250 699.015 Td /F1 9.8 Tf [(Center, which offers a peak performance of 10.7 GFLOPS per optimization process. Roughly 1,000,000 simulations can be )] TJ ET BT 26.250 687.110 Td /F1 9.8 Tf [(done in this time; however, for this relatively small action space, the optimal policy is typically identified within six hours of )] TJ ET BT 26.250 675.205 Td /F1 9.8 Tf [(computation.)] TJ ET BT 26.250 638.603 Td /F4 12.0 Tf [(Results)] TJ ET BT 26.250 618.648 Td /F1 9.8 Tf [(Without antivirals, the expected cumulative number of cases after 12 months is almost 128 million. We found several optimized )] TJ ET BT 26.250 606.744 Td /F1 9.8 Tf [(time-based intervention policies that decrease the spread of disease. Figure 3a shows the comparison of these strategies with a )] TJ ET BT 26.250 594.839 Td /F1 9.8 Tf [(range of naive distribution policies in which fixed fractions of the antiviral stockpile are distributed monthly. Notably, one of these )] TJ ET BT 26.250 582.934 Td /F1 9.8 Tf [(naive policies monthly releases of 5 million regimens pro rata for 10 months consistently performs as well as the optimized )] TJ ET BT 26.250 571.029 Td /F1 9.8 Tf [(policies and better than other naive policies, particularly at uptake rates between 20 % and 60 %. Naive monthly distributions of )] TJ ET BT 26.250 559.125 Td /F1 9.8 Tf [(less than 5 million regimens fail to meet the demand while larger monthly distributions result in greater wastage and rapid )] TJ ET BT 26.250 547.220 Td /F1 9.8 Tf [(exhaustion of the stockpile \(Fig. 3b\).)] TJ ET 0.965 0.965 0.965 rg 26.250 239.713 555.000 297.626 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 537.339 m 581.250 537.339 l 581.250 536.589 l 26.250 536.589 l f 26.250 239.713 m 581.250 239.713 l 581.250 240.463 l 26.250 240.463 l f q 225.000 0 0 139.500 35.250 388.089 cm /I262 Do Q q 35.250 250.963 537.000 131.126 re W n 0.271 0.267 0.267 rg BT 35.250 371.100 Td /F4 9.8 Tf [(Figure 3.)] TJ ET BT 75.888 371.100 Td /F1 9.8 Tf [( Optimizer performance. \(3a\) The optimal policies perform at least as well as the naive strategies of distributing )] TJ ET BT 35.250 357.364 Td /F1 9.8 Tf [(fixed quantities each month until the stockpile is depleted. The four best policies are completely overlapping in the graph: )] TJ ET BT 35.250 343.627 Td /F1 9.8 Tf [(the optimal policy when there is no wastage, the optimal pro rata policy, the optimal policy combining both prevalence-)] TJ ET BT 35.250 329.891 Td /F1 9.8 Tf [(based and pro rata distributions, and the simple strategy of distributing 5M courses per month for ten months. In contrast, )] TJ ET BT 35.250 316.155 Td /F1 9.8 Tf [(the other simple strategies perform poorly for many uptake values. \(3b\) Predicted prevalence curves at an uptake of 50 %. )] TJ ET BT 35.250 302.419 Td /F1 9.8 Tf [(From top to bottom: without intervention, with the optimal intervention policy, releasing 1 million courses every month, )] TJ ET BT 35.250 288.682 Td /F1 9.8 Tf [(releasing 25 million courses in each of the first two months. The dashed lines represent the total number of antivirals )] TJ ET BT 35.250 274.946 Td /F1 9.8 Tf [(distributed and available for treatment. The 1 million per month policy does not release enough antivirals to meet demand; )] TJ ET BT 35.250 261.210 Td /F1 9.8 Tf [(and the 25 million policy leads to a rapid depletion of antivirals, followed by a spike in the number of infections.)] TJ ET Q BT 26.250 222.689 Td /F1 9.8 Tf [(The optimal policy returned by the algorithm is sensitive to the levels of uptake \()] TJ ET q 10.500 0 0 11.250 369.811 220.963 cm /I264 Do Q BT 380.311 222.689 Td /F1 9.8 Tf [(\), but, remarkably, the optimal policies under )] TJ ET BT 26.250 210.784 Td /F1 9.8 Tf [(high levels of wastage \(loss of half of unused supplies every two months\) are predicted to perform as well as optimal policies )] TJ ET BT 26.250 198.879 Td /F1 9.8 Tf [(under no wastage \(Fig. 3a\). Under perfect conditions of no loss or misallocation of antivirals, then there is no reason to reserve )] TJ ET BT 26.250 186.975 Td /F1 9.8 Tf [(the stockpile and the optimal strategies are always a series of large distributions early in the outbreak.)] TJ ET BT 26.250 167.570 Td /F1 9.8 Tf [(A mixed pro rata and prevalence-based distribution policy favored pro rata distributions, particularly for low to intermediate )] TJ ET BT 26.250 155.665 Td /F1 9.8 Tf [(levels of uptake \(Fig. 4a\). This combined with the comparable performance of exclusively pro rata policies \(Fig. 3a\) suggests )] TJ ET BT 26.250 143.760 Td /F1 9.8 Tf [(that prevalence-based distributions are probably unnecessary.)] TJ ET 0.965 0.965 0.965 rg 26.250 -96.371 555.000 230.250 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 133.879 m 581.250 133.879 l 581.250 133.129 l 26.250 133.129 l f q 225.000 0 0 214.500 35.250 -90.371 cm /I266 Do Q q 35.250 -96.371 537.000 0.000 re W n Q Q q 225.000 0 0 139.500 35.250 388.089 cm /I268 Do Q q 225.000 0 0 214.500 35.250 -90.371 cm /I270 Do Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(5)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 466 0 obj << /Type /Annot /Subtype /Link /A 467 0 R /Border [0 0 0] /H /I /Rect [ 35.2500 388.0890 260.2500 527.5890 ] >> endobj 467 0 obj << /Type /Action /S /URI /URI (http://currents.plos.org/influenza/files/2009/11/figure3.png) >> endobj 468 0 obj << /Type /XObject /Subtype /Image /Width 300 /Height 186 /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 1 /Columns 300 /BitsPerComponent 8>> /ColorSpace /DeviceGray /BitsPerComponent 8 /Length 401>> stream xA 0 =fy9뀟\GP endstream endobj 469 0 obj << /Type /XObject /Subtype /Image /Width 300 /Height 186 /SMask 468 0 R /Filter /FlateDecode /DecodeParms << /Predictor 15 /Colors 3 /Columns 300 /BitsPerComponent 8>> /ColorSpace /DeviceRGB /BitsPerComponent 8 /Length 24292>> stream xwt}6|EY($ vĢJ%;K/-ի7>YY-*NM")6PA$HE]`{C3[Rx{̭$IBS.iN +_ & 7+%p3t=MV4`d +9sc,)d9_nub3G8(p,\P"XVĉ,ċBVcLUBa&14/R?O/y+]֭C PB( ~cccfܘ:g9̱ QO.9CL_iqxa~^xg}ꩧfSd4w`W2Y[Qhllq !H J8߸q'͠&f.3!8r7S=xw}g?O?a,͈x޺uJQV<O$E"+W󋋋!z^,3b1E4-<-avڥT*?3B01!.l6pqxASdpby"&" 6mF"I'A܀<>]`NIQ !MaSQLNS#g ^~ųPذaV3h4.> [[A ɘ+:u -[о}Dk*~Q2AGl`0 {70 +**"~FrT*n PK$`= ^'LOЌ _ ,h4@`fsVc6?=Gя< ~`D/6}UV .,))0L"H$v7m[WW' |Rt:Bh)t,quw<I.|衩9:!kB۫294릸=j3pv Ad2P(.\hXy3whN o^ztq{ [y<|zbh4cʄ  H4 !$1 ۱c+mPaH 9Mgzp:aoTlcrX\Nb3I1$vZvB@ D"QWORBॗ`[ʖOWZZzL_.P(0>?pe2 /ڵr EzZm~~~YYE~deTJx113`0TcOI(~SX[ y@ٳgoVOOP(_pb1 r }'WOHT{z@@qN>T*/^h0d2Y[[zjvvvBU S'D"O4{01gn DV\˙Á~,nrJKKH}Ȉ tYVN$BAϮL 444rͦP(\.Wmm-,ry]]@2SСC9;wYfRi2u´/tv09`~)O>IR ( ۪*O͛\hhh0 ƻʲX<0)6%ʌ<0ċΉ)ɓ#P5p44lӂh4O$ѷ'::2`˖)h1PmH& Ss.UT\">OOݕ\.B+B+DB۝_\Ns;@njcrBق /(յk.Ax9D:퍲7xCܹ3B{`0 %srZmƍH'NM<իD%!L஧y Dʑ7S{b)'s`h58hT&4z ֭I=9իQ׍#MMhrUSĸK`2>b;v,''Pkk˩ ?PPP yNL\S^sE7] oc466b?L+ Eݺ9T=B.9Wwt T(ԥ(>p+KM XyI[a&˭Vkvv6eFƘ/gڼBs h>x U_2Aqr2 "8@ ~zAϜJ$,V</̂0Ze t<> b͑ D8L*0eb?Ü຤8~fj`*d}Ɯ&|sqkAm̼g&~Jehoooccp F ^7fd2egg2j2 @U\̴ruuZO__^~1uXX9;L wޑM ܐ$T`zL/'fAlt8h4L&&Y >ynn;Rx8 Bh%(L&AH Óј#TI.s9hƋikk{Wfo[.2~$ L8]k NRqǵSC*zCq:L.>b…֭ۿ$0 хKKB>DyyKۯͦ.-t~&OmSp{Y0mϹQKh$IV(Ɠ],Rq \,~?9LsWww履fGF2 qIZSp,pR myJKK\DhC @[[FI6Q|95J<`6)rPLB8pׯ>~})д|jB鷦Fx&Փ_3ǹ}v!ϧHF555}}}www+k`jԧP룏Xl@gǧ׻BǏ;p`٦DެٜW x:QLrRNSSӪg'NX`AZ !?p@aa!utܜ8o;w/h'އVTS/\H;Bn0 'h(sBu}QΪUB]_|@4p!>xM$P21z3 x<Ǐ0lÆ LFןt P_Rn?˂H$jP(+X\]]i&,@L2t)es𠶲Rf6sr([FAV+8'_mh4t]`ٴLr!駚E99ÜJpb!#TBa;H/ !D{ WJ0+RSSSUUh,=¥l>KʫcFQ4.p#OcAes>3vaj(Kx<ÑSߴG `.Dze U(+Ţ((*X!M/q@RWr 6h `;wpO9|r>xTtbY>O@S(//K, wK\ԟPӳ*M^'bzp`d[$t)jqƍ}>_QQѵk ,| z<Xf B eeeSFb8}7o9xԓl⬂h0 PHj4V$ Q8`l qv|`tWqs'`OUd$bokkolޜFĸq ?P‘ ;y$epir2kxLKvPxV4bׯ!y@pI@J /^ UUUhtALeX ?Mnϟ?-//n[cvBnCC!`~zF`c <ɠZ jR\PY  B]J)g "x}uSpi}\K.YV[la o,>칋x3&B!C8`(/l͛I,***,,DUa6ItG` ?֘|ff39|>`A40VtzPZ Fp2-V* =@=oFXGGu2i yŊ33aB{qݻwfޯxŋ$駟r]Aޕ[74;ʞ2v0Cp1 iö B844Z-HNz###:.#]Xm۶8p$I 1 v;@`p 8d2rr@y9nVjꊎG{l[[㵵O=TɁ~A>7B!`. ۍћZ-0ٌVf3T*wyyԹ-Xloi4AǕ+7GG;:˗1Zz骪X^c|~Atx3+Kx|: b=Uht[wx$xq\.PZJ-fttiRܟ,NP'{3h4*--F,744D~&AH` ^P(,)) B`00N=<19UUU$I"77whh"$zP!B!DB D$0Q'}.rSD! $IQ".$se'8xCɖ Õ@7?_v\B#P!a9 8"$s'̿h{eʪIFko 1 @ȗHrVɓޜի}AChaj'Ub7oY(slIY-[z=JT&+AǏ Br l`gd$¢$@tzߏ\qؘ~|" D"AaÄ"dyyȵ$PpG"}#uii/ RIk׮&B$[2PՎ67S;hWrWߴbZrR=!e~3ڊ My9ܠ"?YEE̢5=QR%p y诧˟[uxiW_}Μ9Cm9p@0/V(̝: .\.W(.]Tl6֭[\$IREV vG 5kTTp8LgX7n&{xT*i}tt; TJDz}N`0JV7E}M׮=(|e _U|}fb%ܸq8keIk&?ƞu,ae@a/q= HGGG׬Y{ !W\O~rJDjnnM:N5k֔TVV5kKRxZZZbFj%///fee|T*---F*J,D"Fc6q%%%%%%/555*iLݽV-JJer&o.QWt>] b. 겲zģ;x(ŲeY+[Vx6 G֬X7jx0׿5LH$#Dpx||<R_~:}tӚؘJ5Ss}#($ITUU1᢯jVWWDxyôiѹd~ϟ?Ӄ0"]W:!x=5$+WuGU!PIAAAN?ccc.]ZnӶ ðSNLʼXG}}t]K.E"UV5Gmn:^ј鶵9tRD"QYY8b`3O]ZmWbt#aꡢawJwޡj5`0tww8Nyf)˗/OJ#Iٳ٩Gz?LͰ$1!lmmlڔdڴ`hQByg ?=-Q#ߘa /,,Q/geeiGZfO<򂂂|0'~%hnn>qDQQ֭[W^yeɒ%G7IOe#WV~_x!CU1*!s2~||"SϘx g!⩊{ e\:rAݞKUœj+WABȝstIaS_fggeM Rgi% &9I9U;sCC<)1c .$d+V1W48ksI$hޖ' I[4miiqݔ+J|rɷW\x<T߿?f "8pZZ~)\ԯq+++|>WC\93yU*ǟyT98}Gj-pi{>dZZPZ@wܙ4!޾};3q fŊH6=]W999޲eˑ#G7t JEVp^&T*=Zʤ"pHWaYÏ=Y`9LlE+OL!T#y#4z+V Mͣ"(s]0Bf\~gΟ??22b4[cr9@єPuuuaAVvN/G.}Ν[d q0jBQc"qNC36Bvҥ?x||BDkX -H$0$ 0>PW_I*1m_m6 >+V$V5 eW_~[shrSᾳkO0Tv#Su6L6za!ljjַꫯ.[`E>qeP(ή\===ǎ.P(EEEeeeԁY3?~Fnw]ImMQs-[[ׯ_gdZ;;[[?0|OROHvZ.v= wwwS;Z-U].WKKFĉկ2`0g;CEM[L&+++cnZFy<Ζw}v⚚e˖Y,z+4!U @Tz~(D'?9rw]pɒ%K,!"EO3״?[\m T<Obuw5p銊N@cX2jW^]|Ν;oUfBj}:/^7aݻT*Z_$M:$H@`H)r 寽?m[Zw|jǙ\U^7{<FyTo!!իO:xA9СC=ثJI;R$o>[65~G}h4_ټy3uB*zO4D< cFǥ88q" Iҍ7V\brf!ﳋCo;.?Ew̿sdBBAkȌ^w8ntZ q(a+#RԳ|^zI.Ӌ՗_~rV^!i 6l8xff|98Yf$I655k}}}jz+VH$xVDcS^'dzo4|AnPI@aI(orޱ8<&$sRUOVYeonY%LMϕ+WD"Qgg'A B$V]JFdN0 8Ǐ? 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UC,6䑪bb\S!.JnHg9rIJN۶=lat&]58OMRٚI@$DI֭[m_v0˲ RBǎ:;dt;y FT0!lfgccc<==Mfrl%w!NWm1rn8+azz:H444)-. z.gnV˼G rwx867lMMMdMCED) wXIWm1e+f1tW81>A=bnbuOaCd(Qǁc#Ȳ#V[+U[]nһr$痾fLXx g״tv0* | U)`q-QN4 mm;쪫L&OOT =裒BRU^F.-sƓ k1mKD50M\A9 0lOf7ԔV PdY ˀus#Zere .]K@i\T\r .,b]ΝbL_BP091qF[[[6OΓ\HEӐH$dcXkk/c'Hᰌ122y'$_RU^ms'eW|"SUP)ײY*m#WȲi";T(DYFKɪSV?Sa%^0\x5cmm-Dh4 U_qOS slll``)4449$Nşnv>o*"t-HaeESUD8bx\(ð[B 6d>7<*GHU/lw i5ţ>$upp;B$džx0Ub>c28Ç>|!X1 V.麭6*HČ!M5h$ 7Xİr ܹ/r;ň2 -Vt`:u\ڛceYկED"uuu֔>aم0>1\eccfgg{{{w.r]/{{ >Lr`Y~?ٰ*PUq ,C($76*$:TT̊ @cɆ@,w׊a .< hmm- lmm̌+XjC.(~L__߭[l{{{OOO"qcc|>dYʕM 4ִih\P- rKc Y(di}]̐c5˻,'' immbB㭭---b6Q`\1u`!^}Rww7D nOOW8!EBaY" *9zt#dĖ<(`Y@3ncpGz7^hm1V+빣h8;PJvYZ*s_jobW/R90K'͉Ns1rvU 8f!Fnwq]v)mCo瓊L&y׿|޶p8/j ~icColTmh=txN _$dƥ" dʾ4:-46B!YlMTUJ$t(͡S]] ٺ1n)/_zj{{{&w[fv} qʴwh4 N¦x$$B0#e T~-y 1lvpppyyI;HSRY1]58U6,*'/xc #bmc²vӐQ@6k m@P:JckS/4R)00$rGYTiyN8#GN> ݴw%v)sGb񨥥!>D@``|$(Ŭ.ΌzKKS]!7}wջQd2ي~HuzR5b޶^z 1E̍`:Wb}O_LR(]}k|>?qqq/_>w+Ybn޼榇7xޟښ#\p7۶H$1SSS[[[333r2۷=⚜_|[e]׽1PU___wTS,0d,ׯ__[[cCLL&SSSlWWWfff)xqqqrrriiQeqy/k !>z7WVV._jjj"~cc~իW\jii ,fss͛`~߯lllLLLܸq#577Kbnݺ裏?]YYY]]OVVV_>::j6\xرcW^x'97۶?ZWWa~۷oONN,棏>Z[[O~xڵD"Aɹp"BD?s,p9AT½0kkkoN&죟'Llhh|_WUujj*H:t&׊q>Qϑ٢fss3ϯ|~>b??k׮ݾ}[4RX___4Mz``0'Xi|@jYL*:eY7o#U_=Oknn1̓ׯ__^^$300tUrY\\L$x|yyC455;wɓW^|oa.\077w`0 :\.mgϞ%k bLBUե%r,###7odC:::$I$V}ʧ8&B_C70rb?svvS{~;.kO"f '1BƍTjK.y*guu&7]yez`*r0}}},˯okk~WGydGr} xREc{R;wuww;3dz_---.]6 #(u0 pRxt0&Q4|>aO6Mer>jRFz衅'N(bY,d3T$I&DqrrҶmIN8E$)ϧ鞞{mWSUvD5!Ahvv̡CP];eT#S>Ч?T+,ehllM02 >UOJx璊p;rk~&x~gklj=2Dz!1 ׿__~$d5[#.wW^y_W/R$ُ Sm%gX^&V>ݧt`sG)Š{9-H11e'Ti)> endobj 501 0 obj << /Length 29701 >> stream q 15.000 32.326 577.500 744.674 re W n 0.965 0.965 0.965 rg 26.250 662.096 555.000 114.904 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 662.096 m 581.250 662.096 l 581.250 662.846 l 26.250 662.846 l f q 35.250 673.346 537.000 103.654 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 4.)] TJ ET BT 75.888 766.011 Td /F1 9.8 Tf [( Optimal policies. \(4a\) Optimal policies combining prevalence-based \(red\) and pro rata distributions \(blue\). Each )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(row gives the optimal sequence of actions for a given value of uptake. \(4b\) Optimal pro rata distributions. \(4c\) Performance )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(of actions for the first \(August\) distribution. Darkness indicates how many times an action was visited during the )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(optimization routine. At a modest and perhaps realistic 20 % uptake, the optimal combined strategy begins with distributing )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(half of the remaining federal stockpile pro rata followed by monthly distributions of 10M proportional to prevalence, 10M pro )] TJ ET BT 35.250 697.330 Td /F1 9.8 Tf [(rata, none, and 5M pro rata. The optimal pro rata policy is an initial distribution of the entire 50M regimens. \(4c\) indicates, )] TJ ET BT 35.250 683.593 Td /F1 9.8 Tf [(however, that, at this uptake rate, all other distribution options are expected to perform similarly.)] TJ ET Q BT 26.250 645.072 Td /F1 9.8 Tf [(The optimal pro rata policies \(Fig. 4b\) vary considerably with uptake. At realistically low levels of uptake \(between 10 % and 25 )] TJ ET BT 26.250 633.168 Td /F1 9.8 Tf [(%\) the optimal strategies are either a single distribution of the entire stockpile or a single distribution of half of the stockpile )] TJ ET BT 26.250 621.263 Td /F1 9.8 Tf [(followed by a slow steady stream of smaller releases. For example, at 15 % uptake, the optimal policy is to distribute a twelve-)] TJ ET BT 26.250 609.358 Td /F1 9.8 Tf [(month sequence of 25M, 1M, 10M, 10M, 1M, 0, 1M, 0, 1M, 0, 1M, and 0 courses. At higher levels of uptake, which are probably )] TJ ET BT 26.250 597.453 Td /F1 9.8 Tf [(unlikely without a national campaign to increase rates of antiviral treatment for mild cases, the optimal strategies are a bit more )] TJ ET BT 26.250 585.549 Td /F1 9.8 Tf [(complex, involving longer series of variable distributions. Between 35 % and 65 % uptake, the optimal strategies involve initial )] TJ ET BT 26.250 573.644 Td /F1 9.8 Tf [(delays of a few months during which only small quantities are distributed. This delay prevents the wastage of antivirals that will )] TJ ET BT 26.250 561.739 Td /F1 9.8 Tf [(go unused during the initial period when prevalence is relatively low. This delay strategy is even more pronounced when )] TJ ET BT 26.250 549.834 Td /F1 9.8 Tf [(optimizing distributions for the entire epidemic period \(Supplementary Information\).)] TJ ET BT 26.250 530.430 Td /F1 9.8 Tf [(The optimization provides information about the relative performance of different actions. At uptake levels less than 25 %, the )] TJ ET BT 26.250 518.525 Td /F1 9.8 Tf [(best strategies are expected to reduce the number of cases by at most 15 %. At even lower levels of uptake \(less than 15 %\), )] TJ ET BT 26.250 506.620 Td /F1 9.8 Tf [(all initial \(August\) pro rata distributions perform equally well because only a very small proportion of the entire stockpile will ever )] TJ ET BT 26.250 494.715 Td /F1 9.8 Tf [(be used to treat H1N1 \(Fig. 4c\). As uptake increases, there is a trade-off between meeting the increasing demand for treatment )] TJ ET BT 26.250 482.811 Td /F1 9.8 Tf [(and risking wastage of courses that would otherwise be used to treat future cases of H1N1. Between 20 % and 30 % uptake, )] TJ ET BT 26.250 470.906 Td /F1 9.8 Tf [(the benefits of increased coverage outweigh the consequent wastage, and thus the optimal action is a large release in August. )] TJ ET BT 26.250 459.001 Td /F1 9.8 Tf [(Between 35 % and 60 %, wasted courses are more likely to have been used for future treatment, suggesting a steady )] TJ ET BT 26.250 447.096 Td /F1 9.8 Tf [(distribution throughout the 12 month period \(Fig. 4b\). At uptake greater than 60 %, an overwhelming fraction of infected )] TJ ET BT 26.250 435.192 Td /F1 9.8 Tf [(individuals seek treatment, and any distribution schedule effectively mitigates the epidemic for 12 months.)] TJ ET BT 26.250 398.589 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 378.635 Td /F1 9.8 Tf [(Since avian influenza H5N1 became a potential public health threat in 2003, public health agencies around the globe have been )] TJ ET BT 26.250 366.730 Td /F1 9.8 Tf [(diligently planning for the next influenza pandemic. While the concerted response to H1N1 reflects this careful preparation, )] TJ ET BT 26.250 354.825 Td /F1 9.8 Tf [(several expected and unexpeted events, including its apparent North American origin, the rapid overburdening of U.S. )] TJ ET BT 26.250 342.921 Td /F1 9.8 Tf [(laboratory capacity, non-uniform testing and treatment policies among U.S. states, and delays in production of a viable vaccine, )] TJ ET BT 26.250 331.016 Td /F1 9.8 Tf [(all reinforce the need for a dynamic and quantitative playbook for pandemic mitigation using pharmaceutical countermeasures.)] TJ ET BT 26.250 311.611 Td /F1 9.8 Tf [(By adapting an established algorithm to optimize disease mitigation policies, we advance from the traditional candidate strategy )] TJ ET BT 26.250 299.706 Td /F1 9.8 Tf [(approach to rapid and systematic analysis of numerous policy options. This is just one of many possible optimization methods )] TJ ET BT 26.250 287.802 Td /F1 9.8 Tf [(suitable for this purpose )] TJ ET 0.267 0.267 0.267 rg BT 132.466 287.802 Td /F1 9.8 Tf [([27])] TJ ET BT 148.730 287.802 Td /F1 9.8 Tf [([28])] TJ ET BT 164.993 287.802 Td /F1 9.8 Tf [([29])] TJ ET BT 181.256 287.802 Td /F1 9.8 Tf [([30])] TJ ET 0.271 0.267 0.267 rg BT 197.519 287.802 Td /F1 9.8 Tf [( . Our choice of UCT was based on the insight that, with some careful modeling, disease )] TJ ET BT 26.250 275.897 Td /F1 9.8 Tf [(intervention strategies can be nicely mapped onto policy trees and that this approach can be coupled to any stochastic epidemic )] TJ ET BT 26.250 263.992 Td /F1 9.8 Tf [(model. This approach has performed successfully on large policy trees )] TJ ET 0.267 0.267 0.267 rg BT 333.492 263.992 Td /F1 9.8 Tf [([31])] TJ ET 0.271 0.267 0.267 rg BT 349.755 263.992 Td /F1 9.8 Tf [( and has favorable convergence properties )] TJ ET 0.267 0.267 0.267 rg BT 537.267 263.992 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 553.530 263.992 Td /F1 9.8 Tf [( . In )] TJ ET BT 26.250 252.087 Td /F1 9.8 Tf [(particular, it is guaranteed to converge on the optimal policy eventually, unlike simulated annealing and genetic algorithms. We )] TJ ET BT 26.250 240.183 Td /F1 9.8 Tf [(do not claim that the optimized antiviral strategies \(Fig. 4\) are necessarily the best possible. Rather, we simply argue that in a )] TJ ET BT 26.250 228.278 Td /F1 9.8 Tf [(reasonable amount of time, the model converged on policies that are predicted to perform equal to or better than obvious )] TJ ET BT 26.250 216.373 Td /F1 9.8 Tf [(candidate policies, and that the resulting policies make intuitive sense.)] TJ ET BT 26.250 196.968 Td /F1 9.8 Tf [(Unexpectedly, our analysis suggests that the optimal distribution schedule for the U.S. national antiviral stockpile may be quite )] TJ ET BT 26.250 185.064 Td /F1 9.8 Tf [(simple. A monthly distribution of 5 million regimens to states consistently matches or outperforms other policy options, )] TJ ET BT 26.250 173.159 Td /F1 9.8 Tf [(regardless of the level of uptake or rate of misuse \(Fig. 3a\). Slight variations on this policy, for example, regular distributions of )] TJ ET BT 26.250 161.254 Td /F1 9.8 Tf [(1M or 10M courses are predicted to perform significantly worse at intermediate levels of uptake. Since there can be many )] TJ ET BT 26.250 149.349 Td /F1 9.8 Tf [(optimal policies, the results of the optimization algorithm do not necessarily have the same simple structure as the 5M strategy. )] TJ ET BT 26.250 137.445 Td /F1 9.8 Tf [(Our optimization allowed for the possibility of distributions proportional to prevalence, although such actions are not consistent )] TJ ET BT 26.250 125.540 Td /F1 9.8 Tf [(with the current strategic national stockpile policy and would likely be both politically and logistically difficult. Notably, the results )] TJ ET BT 26.250 113.635 Td /F1 9.8 Tf [(suggest that prevalence-based distributions are not expected to enhance the impact of antivirals.)] TJ ET BT 26.250 94.230 Td /F1 9.8 Tf [(The expected impact of this simple 5 million course monthly distribution schedule is highly sensitive to the rate of antiviral )] TJ ET BT 26.250 82.326 Td /F1 9.8 Tf [(treatment \()] TJ ET q 10.500 0 0 11.250 73.391 80.599 cm /I272 Do Q BT 83.891 82.326 Td /F1 9.8 Tf [(\). From an ongoing study of H1N1 antiviral uptake in Milwaukee, preliminary estimates of the fraction of reported )] TJ ET BT 26.250 70.421 Td /F1 9.8 Tf [(cases receiving treatment within 48 hours of developing symptoms are less than 20 % )] TJ ET 0.267 0.267 0.267 rg BT 399.616 70.421 Td /F1 9.8 Tf [([32])] TJ ET 0.271 0.267 0.267 rg BT 415.879 70.421 Td /F1 9.8 Tf [(. This suggests that we are likely in )] TJ ET BT 26.250 58.516 Td /F1 9.8 Tf [(the range where all strategies perform equally poorly and are predicted to minimally mitigate transmission. Although treatment )] TJ ET BT 26.250 46.611 Td /F1 9.8 Tf [(beyond 48 hours may not alter clinical course, there is some evidence that it may lead to a more rapid drop-off in viral shedding )] TJ ET Q q 15.000 32.326 577.500 744.674 re W n 0.965 0.965 0.965 rg 26.250 662.096 555.000 114.904 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 662.096 m 581.250 662.096 l 581.250 662.846 l 26.250 662.846 l f q 35.250 673.346 537.000 103.654 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 4.)] TJ ET BT 75.888 766.011 Td /F1 9.8 Tf [( Optimal policies. \(4a\) Optimal policies combining prevalence-based \(red\) and pro rata distributions \(blue\). Each )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(row gives the optimal sequence of actions for a given value of uptake. \(4b\) Optimal pro rata distributions. \(4c\) Performance )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(of actions for the first \(August\) distribution. Darkness indicates how many times an action was visited during the )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(optimization routine. At a modest and perhaps realistic 20 % uptake, the optimal combined strategy begins with distributing )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(half of the remaining federal stockpile pro rata followed by monthly distributions of 10M proportional to prevalence, 10M pro )] TJ ET BT 35.250 697.330 Td /F1 9.8 Tf [(rata, none, and 5M pro rata. The optimal pro rata policy is an initial distribution of the entire 50M regimens. \(4c\) indicates, )] TJ ET BT 35.250 683.593 Td /F1 9.8 Tf [(however, that, at this uptake rate, all other distribution options are expected to perform similarly.)] TJ ET Q BT 26.250 645.072 Td /F1 9.8 Tf [(The optimal pro rata policies \(Fig. 4b\) vary considerably with uptake. At realistically low levels of uptake \(between 10 % and 25 )] TJ ET BT 26.250 633.168 Td /F1 9.8 Tf [(%\) the optimal strategies are either a single distribution of the entire stockpile or a single distribution of half of the stockpile )] TJ ET BT 26.250 621.263 Td /F1 9.8 Tf [(followed by a slow steady stream of smaller releases. For example, at 15 % uptake, the optimal policy is to distribute a twelve-)] TJ ET BT 26.250 609.358 Td /F1 9.8 Tf [(month sequence of 25M, 1M, 10M, 10M, 1M, 0, 1M, 0, 1M, 0, 1M, and 0 courses. At higher levels of uptake, which are probably )] TJ ET BT 26.250 597.453 Td /F1 9.8 Tf [(unlikely without a national campaign to increase rates of antiviral treatment for mild cases, the optimal strategies are a bit more )] TJ ET BT 26.250 585.549 Td /F1 9.8 Tf [(complex, involving longer series of variable distributions. Between 35 % and 65 % uptake, the optimal strategies involve initial )] TJ ET BT 26.250 573.644 Td /F1 9.8 Tf [(delays of a few months during which only small quantities are distributed. This delay prevents the wastage of antivirals that will )] TJ ET BT 26.250 561.739 Td /F1 9.8 Tf [(go unused during the initial period when prevalence is relatively low. This delay strategy is even more pronounced when )] TJ ET BT 26.250 549.834 Td /F1 9.8 Tf [(optimizing distributions for the entire epidemic period \(Supplementary Information\).)] TJ ET BT 26.250 530.430 Td /F1 9.8 Tf [(The optimization provides information about the relative performance of different actions. At uptake levels less than 25 %, the )] TJ ET BT 26.250 518.525 Td /F1 9.8 Tf [(best strategies are expected to reduce the number of cases by at most 15 %. At even lower levels of uptake \(less than 15 %\), )] TJ ET BT 26.250 506.620 Td /F1 9.8 Tf [(all initial \(August\) pro rata distributions perform equally well because only a very small proportion of the entire stockpile will ever )] TJ ET BT 26.250 494.715 Td /F1 9.8 Tf [(be used to treat H1N1 \(Fig. 4c\). As uptake increases, there is a trade-off between meeting the increasing demand for treatment )] TJ ET BT 26.250 482.811 Td /F1 9.8 Tf [(and risking wastage of courses that would otherwise be used to treat future cases of H1N1. Between 20 % and 30 % uptake, )] TJ ET BT 26.250 470.906 Td /F1 9.8 Tf [(the benefits of increased coverage outweigh the consequent wastage, and thus the optimal action is a large release in August. )] TJ ET BT 26.250 459.001 Td /F1 9.8 Tf [(Between 35 % and 60 %, wasted courses are more likely to have been used for future treatment, suggesting a steady )] TJ ET BT 26.250 447.096 Td /F1 9.8 Tf [(distribution throughout the 12 month period \(Fig. 4b\). At uptake greater than 60 %, an overwhelming fraction of infected )] TJ ET BT 26.250 435.192 Td /F1 9.8 Tf [(individuals seek treatment, and any distribution schedule effectively mitigates the epidemic for 12 months.)] TJ ET BT 26.250 398.589 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 378.635 Td /F1 9.8 Tf [(Since avian influenza H5N1 became a potential public health threat in 2003, public health agencies around the globe have been )] TJ ET BT 26.250 366.730 Td /F1 9.8 Tf [(diligently planning for the next influenza pandemic. While the concerted response to H1N1 reflects this careful preparation, )] TJ ET BT 26.250 354.825 Td /F1 9.8 Tf [(several expected and unexpeted events, including its apparent North American origin, the rapid overburdening of U.S. )] TJ ET BT 26.250 342.921 Td /F1 9.8 Tf [(laboratory capacity, non-uniform testing and treatment policies among U.S. states, and delays in production of a viable vaccine, )] TJ ET BT 26.250 331.016 Td /F1 9.8 Tf [(all reinforce the need for a dynamic and quantitative playbook for pandemic mitigation using pharmaceutical countermeasures.)] TJ ET BT 26.250 311.611 Td /F1 9.8 Tf [(By adapting an established algorithm to optimize disease mitigation policies, we advance from the traditional candidate strategy )] TJ ET BT 26.250 299.706 Td /F1 9.8 Tf [(approach to rapid and systematic analysis of numerous policy options. This is just one of many possible optimization methods )] TJ ET BT 26.250 287.802 Td /F1 9.8 Tf [(suitable for this purpose )] TJ ET 0.267 0.267 0.267 rg BT 132.466 287.802 Td /F1 9.8 Tf [([27])] TJ ET BT 148.730 287.802 Td /F1 9.8 Tf [([28])] TJ ET BT 164.993 287.802 Td /F1 9.8 Tf [([29])] TJ ET BT 181.256 287.802 Td /F1 9.8 Tf [([30])] TJ ET 0.271 0.267 0.267 rg BT 197.519 287.802 Td /F1 9.8 Tf [( . Our choice of UCT was based on the insight that, with some careful modeling, disease )] TJ ET BT 26.250 275.897 Td /F1 9.8 Tf [(intervention strategies can be nicely mapped onto policy trees and that this approach can be coupled to any stochastic epidemic )] TJ ET BT 26.250 263.992 Td /F1 9.8 Tf [(model. This approach has performed successfully on large policy trees )] TJ ET 0.267 0.267 0.267 rg BT 333.492 263.992 Td /F1 9.8 Tf [([31])] TJ ET 0.271 0.267 0.267 rg BT 349.755 263.992 Td /F1 9.8 Tf [( and has favorable convergence properties )] TJ ET 0.267 0.267 0.267 rg BT 537.267 263.992 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 553.530 263.992 Td /F1 9.8 Tf [( . In )] TJ ET BT 26.250 252.087 Td /F1 9.8 Tf [(particular, it is guaranteed to converge on the optimal policy eventually, unlike simulated annealing and genetic algorithms. We )] TJ ET BT 26.250 240.183 Td /F1 9.8 Tf [(do not claim that the optimized antiviral strategies \(Fig. 4\) are necessarily the best possible. Rather, we simply argue that in a )] TJ ET BT 26.250 228.278 Td /F1 9.8 Tf [(reasonable amount of time, the model converged on policies that are predicted to perform equal to or better than obvious )] TJ ET BT 26.250 216.373 Td /F1 9.8 Tf [(candidate policies, and that the resulting policies make intuitive sense.)] TJ ET BT 26.250 196.968 Td /F1 9.8 Tf [(Unexpectedly, our analysis suggests that the optimal distribution schedule for the U.S. national antiviral stockpile may be quite )] TJ ET BT 26.250 185.064 Td /F1 9.8 Tf [(simple. A monthly distribution of 5 million regimens to states consistently matches or outperforms other policy options, )] TJ ET BT 26.250 173.159 Td /F1 9.8 Tf [(regardless of the level of uptake or rate of misuse \(Fig. 3a\). Slight variations on this policy, for example, regular distributions of )] TJ ET BT 26.250 161.254 Td /F1 9.8 Tf [(1M or 10M courses are predicted to perform significantly worse at intermediate levels of uptake. Since there can be many )] TJ ET BT 26.250 149.349 Td /F1 9.8 Tf [(optimal policies, the results of the optimization algorithm do not necessarily have the same simple structure as the 5M strategy. )] TJ ET BT 26.250 137.445 Td /F1 9.8 Tf [(Our optimization allowed for the possibility of distributions proportional to prevalence, although such actions are not consistent )] TJ ET BT 26.250 125.540 Td /F1 9.8 Tf [(with the current strategic national stockpile policy and would likely be both politically and logistically difficult. Notably, the results )] TJ ET BT 26.250 113.635 Td /F1 9.8 Tf [(suggest that prevalence-based distributions are not expected to enhance the impact of antivirals.)] TJ ET BT 26.250 94.230 Td /F1 9.8 Tf [(The expected impact of this simple 5 million course monthly distribution schedule is highly sensitive to the rate of antiviral )] TJ ET BT 26.250 82.326 Td /F1 9.8 Tf [(treatment \()] TJ ET q 10.500 0 0 11.250 73.391 80.599 cm /I274 Do Q BT 83.891 82.326 Td /F1 9.8 Tf [(\). From an ongoing study of H1N1 antiviral uptake in Milwaukee, preliminary estimates of the fraction of reported )] TJ ET BT 26.250 70.421 Td /F1 9.8 Tf [(cases receiving treatment within 48 hours of developing symptoms are less than 20 % )] TJ ET 0.267 0.267 0.267 rg BT 399.616 70.421 Td /F1 9.8 Tf [([32])] TJ ET 0.271 0.267 0.267 rg BT 415.879 70.421 Td /F1 9.8 Tf [(. This suggests that we are likely in )] TJ ET BT 26.250 58.516 Td /F1 9.8 Tf [(the range where all strategies perform equally poorly and are predicted to minimally mitigate transmission. Although treatment )] TJ ET BT 26.250 46.611 Td /F1 9.8 Tf [(beyond 48 hours may not alter clinical course, there is some evidence that it may lead to a more rapid drop-off in viral shedding )] TJ ET Q q 15.000 32.326 577.500 744.674 re W n 0.965 0.965 0.965 rg 26.250 662.096 555.000 114.904 re f 0.267 0.267 0.267 rg 0.267 0.267 0.267 RG 26.250 662.096 m 581.250 662.096 l 581.250 662.846 l 26.250 662.846 l f q 35.250 673.346 537.000 103.654 re W n 0.271 0.267 0.267 rg BT 35.250 766.011 Td /F4 9.8 Tf [(Figure 4.)] TJ ET BT 75.888 766.011 Td /F1 9.8 Tf [( Optimal policies. \(4a\) Optimal policies combining prevalence-based \(red\) and pro rata distributions \(blue\). Each )] TJ ET BT 35.250 752.275 Td /F1 9.8 Tf [(row gives the optimal sequence of actions for a given value of uptake. \(4b\) Optimal pro rata distributions. \(4c\) Performance )] TJ ET BT 35.250 738.538 Td /F1 9.8 Tf [(of actions for the first \(August\) distribution. Darkness indicates how many times an action was visited during the )] TJ ET BT 35.250 724.802 Td /F1 9.8 Tf [(optimization routine. At a modest and perhaps realistic 20 % uptake, the optimal combined strategy begins with distributing )] TJ ET BT 35.250 711.066 Td /F1 9.8 Tf [(half of the remaining federal stockpile pro rata followed by monthly distributions of 10M proportional to prevalence, 10M pro )] TJ ET BT 35.250 697.330 Td /F1 9.8 Tf [(rata, none, and 5M pro rata. The optimal pro rata policy is an initial distribution of the entire 50M regimens. \(4c\) indicates, )] TJ ET BT 35.250 683.593 Td /F1 9.8 Tf [(however, that, at this uptake rate, all other distribution options are expected to perform similarly.)] TJ ET Q BT 26.250 645.072 Td /F1 9.8 Tf [(The optimal pro rata policies \(Fig. 4b\) vary considerably with uptake. At realistically low levels of uptake \(between 10 % and 25 )] TJ ET BT 26.250 633.168 Td /F1 9.8 Tf [(%\) the optimal strategies are either a single distribution of the entire stockpile or a single distribution of half of the stockpile )] TJ ET BT 26.250 621.263 Td /F1 9.8 Tf [(followed by a slow steady stream of smaller releases. For example, at 15 % uptake, the optimal policy is to distribute a twelve-)] TJ ET BT 26.250 609.358 Td /F1 9.8 Tf [(month sequence of 25M, 1M, 10M, 10M, 1M, 0, 1M, 0, 1M, 0, 1M, and 0 courses. At higher levels of uptake, which are probably )] TJ ET BT 26.250 597.453 Td /F1 9.8 Tf [(unlikely without a national campaign to increase rates of antiviral treatment for mild cases, the optimal strategies are a bit more )] TJ ET BT 26.250 585.549 Td /F1 9.8 Tf [(complex, involving longer series of variable distributions. Between 35 % and 65 % uptake, the optimal strategies involve initial )] TJ ET BT 26.250 573.644 Td /F1 9.8 Tf [(delays of a few months during which only small quantities are distributed. This delay prevents the wastage of antivirals that will )] TJ ET BT 26.250 561.739 Td /F1 9.8 Tf [(go unused during the initial period when prevalence is relatively low. This delay strategy is even more pronounced when )] TJ ET BT 26.250 549.834 Td /F1 9.8 Tf [(optimizing distributions for the entire epidemic period \(Supplementary Information\).)] TJ ET BT 26.250 530.430 Td /F1 9.8 Tf [(The optimization provides information about the relative performance of different actions. At uptake levels less than 25 %, the )] TJ ET BT 26.250 518.525 Td /F1 9.8 Tf [(best strategies are expected to reduce the number of cases by at most 15 %. At even lower levels of uptake \(less than 15 %\), )] TJ ET BT 26.250 506.620 Td /F1 9.8 Tf [(all initial \(August\) pro rata distributions perform equally well because only a very small proportion of the entire stockpile will ever )] TJ ET BT 26.250 494.715 Td /F1 9.8 Tf [(be used to treat H1N1 \(Fig. 4c\). As uptake increases, there is a trade-off between meeting the increasing demand for treatment )] TJ ET BT 26.250 482.811 Td /F1 9.8 Tf [(and risking wastage of courses that would otherwise be used to treat future cases of H1N1. Between 20 % and 30 % uptake, )] TJ ET BT 26.250 470.906 Td /F1 9.8 Tf [(the benefits of increased coverage outweigh the consequent wastage, and thus the optimal action is a large release in August. )] TJ ET BT 26.250 459.001 Td /F1 9.8 Tf [(Between 35 % and 60 %, wasted courses are more likely to have been used for future treatment, suggesting a steady )] TJ ET BT 26.250 447.096 Td /F1 9.8 Tf [(distribution throughout the 12 month period \(Fig. 4b\). At uptake greater than 60 %, an overwhelming fraction of infected )] TJ ET BT 26.250 435.192 Td /F1 9.8 Tf [(individuals seek treatment, and any distribution schedule effectively mitigates the epidemic for 12 months.)] TJ ET BT 26.250 398.589 Td /F4 12.0 Tf [(Discussion)] TJ ET BT 26.250 378.635 Td /F1 9.8 Tf [(Since avian influenza H5N1 became a potential public health threat in 2003, public health agencies around the globe have been )] TJ ET BT 26.250 366.730 Td /F1 9.8 Tf [(diligently planning for the next influenza pandemic. While the concerted response to H1N1 reflects this careful preparation, )] TJ ET BT 26.250 354.825 Td /F1 9.8 Tf [(several expected and unexpeted events, including its apparent North American origin, the rapid overburdening of U.S. )] TJ ET BT 26.250 342.921 Td /F1 9.8 Tf [(laboratory capacity, non-uniform testing and treatment policies among U.S. states, and delays in production of a viable vaccine, )] TJ ET BT 26.250 331.016 Td /F1 9.8 Tf [(all reinforce the need for a dynamic and quantitative playbook for pandemic mitigation using pharmaceutical countermeasures.)] TJ ET BT 26.250 311.611 Td /F1 9.8 Tf [(By adapting an established algorithm to optimize disease mitigation policies, we advance from the traditional candidate strategy )] TJ ET BT 26.250 299.706 Td /F1 9.8 Tf [(approach to rapid and systematic analysis of numerous policy options. This is just one of many possible optimization methods )] TJ ET BT 26.250 287.802 Td /F1 9.8 Tf [(suitable for this purpose )] TJ ET 0.267 0.267 0.267 rg BT 132.466 287.802 Td /F1 9.8 Tf [([27])] TJ ET BT 148.730 287.802 Td /F1 9.8 Tf [([28])] TJ ET BT 164.993 287.802 Td /F1 9.8 Tf [([29])] TJ ET BT 181.256 287.802 Td /F1 9.8 Tf [([30])] TJ ET 0.271 0.267 0.267 rg BT 197.519 287.802 Td /F1 9.8 Tf [( . Our choice of UCT was based on the insight that, with some careful modeling, disease )] TJ ET BT 26.250 275.897 Td /F1 9.8 Tf [(intervention strategies can be nicely mapped onto policy trees and that this approach can be coupled to any stochastic epidemic )] TJ ET BT 26.250 263.992 Td /F1 9.8 Tf [(model. This approach has performed successfully on large policy trees )] TJ ET 0.267 0.267 0.267 rg BT 333.492 263.992 Td /F1 9.8 Tf [([31])] TJ ET 0.271 0.267 0.267 rg BT 349.755 263.992 Td /F1 9.8 Tf [( and has favorable convergence properties )] TJ ET 0.267 0.267 0.267 rg BT 537.267 263.992 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 553.530 263.992 Td /F1 9.8 Tf [( . In )] TJ ET BT 26.250 252.087 Td /F1 9.8 Tf [(particular, it is guaranteed to converge on the optimal policy eventually, unlike simulated annealing and genetic algorithms. We )] TJ ET BT 26.250 240.183 Td /F1 9.8 Tf [(do not claim that the optimized antiviral strategies \(Fig. 4\) are necessarily the best possible. Rather, we simply argue that in a )] TJ ET BT 26.250 228.278 Td /F1 9.8 Tf [(reasonable amount of time, the model converged on policies that are predicted to perform equal to or better than obvious )] TJ ET BT 26.250 216.373 Td /F1 9.8 Tf [(candidate policies, and that the resulting policies make intuitive sense.)] TJ ET BT 26.250 196.968 Td /F1 9.8 Tf [(Unexpectedly, our analysis suggests that the optimal distribution schedule for the U.S. national antiviral stockpile may be quite )] TJ ET BT 26.250 185.064 Td /F1 9.8 Tf [(simple. A monthly distribution of 5 million regimens to states consistently matches or outperforms other policy options, )] TJ ET BT 26.250 173.159 Td /F1 9.8 Tf [(regardless of the level of uptake or rate of misuse \(Fig. 3a\). Slight variations on this policy, for example, regular distributions of )] TJ ET BT 26.250 161.254 Td /F1 9.8 Tf [(1M or 10M courses are predicted to perform significantly worse at intermediate levels of uptake. Since there can be many )] TJ ET BT 26.250 149.349 Td /F1 9.8 Tf [(optimal policies, the results of the optimization algorithm do not necessarily have the same simple structure as the 5M strategy. )] TJ ET BT 26.250 137.445 Td /F1 9.8 Tf [(Our optimization allowed for the possibility of distributions proportional to prevalence, although such actions are not consistent )] TJ ET BT 26.250 125.540 Td /F1 9.8 Tf [(with the current strategic national stockpile policy and would likely be both politically and logistically difficult. Notably, the results )] TJ ET BT 26.250 113.635 Td /F1 9.8 Tf [(suggest that prevalence-based distributions are not expected to enhance the impact of antivirals.)] TJ ET BT 26.250 94.230 Td /F1 9.8 Tf [(The expected impact of this simple 5 million course monthly distribution schedule is highly sensitive to the rate of antiviral )] TJ ET BT 26.250 82.326 Td /F1 9.8 Tf [(treatment \()] TJ ET q 10.500 0 0 11.250 73.391 80.599 cm /I276 Do Q BT 83.891 82.326 Td /F1 9.8 Tf [(\). From an ongoing study of H1N1 antiviral uptake in Milwaukee, preliminary estimates of the fraction of reported )] TJ ET BT 26.250 70.421 Td /F1 9.8 Tf [(cases receiving treatment within 48 hours of developing symptoms are less than 20 % )] TJ ET 0.267 0.267 0.267 rg BT 399.616 70.421 Td /F1 9.8 Tf [([32])] TJ ET 0.271 0.267 0.267 rg BT 415.879 70.421 Td /F1 9.8 Tf [(. This suggests that we are likely in )] TJ ET BT 26.250 58.516 Td /F1 9.8 Tf [(the range where all strategies perform equally poorly and are predicted to minimally mitigate transmission. 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144.917 767.476 Td /F1 9.8 Tf [([26])] TJ ET 0.271 0.267 0.267 rg BT 161.180 767.476 Td /F1 9.8 Tf [(. Thus public health measures to increase the usage of antivirals for H1N1 have the potential to )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(slow transmission prior to the availability of H1N1 vaccine, but the impact of such measures will critically depend on the )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(Strategic National Stockpile distribution schedule. Although antivirals may not reduce transmission at current levels of uptake, )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(they can significantly reduce morbidity and mortality associated with H1N1 when used to treat potentially severe cases.)] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(Our analysis did not consider the threat of antiviral resistance. Currently circulating strains of seasonal influenza have acquired )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(resistance to oseltamivir )] TJ ET 0.267 0.267 0.267 rg BT 133.529 700.452 Td /F1 9.8 Tf [([33])] TJ ET 0.271 0.267 0.267 rg BT 149.792 700.452 Td /F1 9.8 Tf [( and there is evidence that H1N1 has exhibited this resistance as well )] TJ ET 0.267 0.267 0.267 rg BT 452.179 700.452 Td /F1 9.8 Tf [([34])] TJ ET 0.271 0.267 0.267 rg BT 468.442 700.452 Td /F1 9.8 Tf [( . We also did not )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(incorporate the use of antivirals for prophylaxis, the future availability of vaccines, simultaneous use of NPIs like school )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(closures, or the option of targeting the stockpile towards particular demographic groups, all of which are likely important and )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(may influence the optimal policy.)] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(From rapid genetic sequence analysis to automated syndromic surveillance systems, public health emergency response is )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(rapidly improving in technical capabilities both in the U.S. and worldwide; the rapid response to and characterization of the novel )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(pandemic influenza A \(H1N1\) virus is a testament to this. However, planning the policies of public health response to such )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(identified and emergent threats remains a highly non-quantitative endeavor. We present here a policy optimization approach )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(that is highly modular and can be easily adapted to address multiple additional issues. Our hope is that the quantitative methods )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(will assist clinical experts in developing effective policies to mitigate H1N1 using a combined arsenal of vaccines, antivirals and )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(NPIs. Specifically, a very similar analysis can be used at the international level to optimize global allocation of the WHOs )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(limited antiviral stockpile to resource-poor countries. One can substitute any stochastic model of disease transmission, at any )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(scale, for our national-scale, U.S. H1N1 model. In addition, while the optimization algorithm is particularly well suited for time-)] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(based interventions, any well-behaved policy space can be used )] TJ ET 0.267 0.267 0.267 rg BT 306.972 538.191 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 323.235 538.191 Td /F1 9.8 Tf [( . The approach should thereby facilitate a more )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(comprehensive consideration of pandemic policy options, and will perhaps confirm the efficacy of the current policy or suggest )] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(more strategic options for the future )] TJ ET 0.267 0.267 0.267 rg BT 182.864 514.381 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 199.127 514.381 Td /F1 9.8 Tf [( . The approach should thereby facilitate a more comprehensive consideration of )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(pandemic policy options, and will perhaps confirm the efficacy of the current policy or suggest more strategic options for the )] TJ ET BT 26.250 490.572 Td /F1 9.8 Tf [(future.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 453.969 Td /F4 12.0 Tf [(Supplemental Analysis)] TJ ET BT 26.250 416.817 Td /F4 12.0 Tf [(Supplemental Visualization)] TJ ET 0.271 0.267 0.267 rg BT 26.250 379.665 Td /F4 12.0 Tf [(Acknowledgments)] TJ ET BT 26.250 359.711 Td /F1 9.8 Tf [(The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the )] TJ ET BT 26.250 347.806 Td /F1 9.8 Tf [(Centers for Disease Control and Prevention. The authors thank John Tegeris at BARDA for providing up-to-date information )] TJ ET BT 26.250 335.901 Td /F1 9.8 Tf [(about the U.S. federal and state Strategic National Stockpiles of antivirals, the BARDA flu vaccine group for providing up-to-date )] TJ ET BT 26.250 323.997 Td /F1 9.8 Tf [(estimates for the availability of H1N1 vaccines, the City of Milwaukee Health Department and the Harvard Center for )] TJ ET BT 26.250 312.092 Td /F1 9.8 Tf [(Communicable Disease Dynamics for sharing unpublished data on the receipt of oseltamivir in Milwaukee. The authors )] TJ ET BT 26.250 300.187 Td /F1 9.8 Tf [(acknowledge the Texas Advanced Computing Center \(TACC\) at The University of Texas at Austin \(http://www.tacc.utexas.edu\) )] TJ ET BT 26.250 288.282 Td /F1 9.8 Tf [(for providing HPC resources that have contributed to the research results reported within this paper.)] TJ ET BT 26.250 251.680 Td /F4 12.0 Tf [(Funding Information)] TJ ET BT 26.250 231.726 Td /F1 9.8 Tf [(This work was supported by grants to LM from NIH Models of Infectious Disease Agent Study \(MIDAS\) \(U01-GM087719-01\), )] TJ ET BT 26.250 219.821 Td /F1 9.8 Tf [(the James S. McDonnell Foundation, and NSF \(DEB-0749097\) and grants to BP from CIHR \(PTL-97125 and PAP-93425\) and )] TJ ET BT 26.250 207.916 Td /F1 9.8 Tf [(the Michael Smith Foundation for Health Research.)] TJ ET BT 26.250 171.314 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 151.359 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 114.757 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 87.303 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 87.303 Td /F1 9.8 Tf [(US Centers for Disease Control \(2009\). CDC health update: Swine influenza A \(H1N1\) update: New interim )] TJ ET BT 26.250 75.398 Td /F1 9.8 Tf [(recommendations and guidance for health directors about strategic national stockpile material. )] TJ ET BT 26.250 63.493 Td /F1 9.8 Tf [(http://www.cdc.gov/h1n1flu/HAN/042609.htm.)] TJ ET BT 26.250 44.088 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 44.088 Td /F1 9.8 Tf [(Department of Health and Human Services \(2009\) National framework for 2009-H1N1 influenza preparedness and response.)] TJ ET Q q 15.000 34.207 577.500 742.793 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(thus reducing transmission )] TJ ET 0.267 0.267 0.267 rg BT 144.917 767.476 Td /F1 9.8 Tf [([26])] TJ ET 0.271 0.267 0.267 rg BT 161.180 767.476 Td /F1 9.8 Tf [(. Thus public health measures to increase the usage of antivirals for H1N1 have the potential to )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(slow transmission prior to the availability of H1N1 vaccine, but the impact of such measures will critically depend on the )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(Strategic National Stockpile distribution schedule. Although antivirals may not reduce transmission at current levels of uptake, )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(they can significantly reduce morbidity and mortality associated with H1N1 when used to treat potentially severe cases.)] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(Our analysis did not consider the threat of antiviral resistance. Currently circulating strains of seasonal influenza have acquired )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(resistance to oseltamivir )] TJ ET 0.267 0.267 0.267 rg BT 133.529 700.452 Td /F1 9.8 Tf [([33])] TJ ET 0.271 0.267 0.267 rg BT 149.792 700.452 Td /F1 9.8 Tf [( and there is evidence that H1N1 has exhibited this resistance as well )] TJ ET 0.267 0.267 0.267 rg BT 452.179 700.452 Td /F1 9.8 Tf [([34])] TJ ET 0.271 0.267 0.267 rg BT 468.442 700.452 Td /F1 9.8 Tf [( . We also did not )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(incorporate the use of antivirals for prophylaxis, the future availability of vaccines, simultaneous use of NPIs like school )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(closures, or the option of targeting the stockpile towards particular demographic groups, all of which are likely important and )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(may influence the optimal policy.)] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(From rapid genetic sequence analysis to automated syndromic surveillance systems, public health emergency response is )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(rapidly improving in technical capabilities both in the U.S. and worldwide; the rapid response to and characterization of the novel )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(pandemic influenza A \(H1N1\) virus is a testament to this. However, planning the policies of public health response to such )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(identified and emergent threats remains a highly non-quantitative endeavor. We present here a policy optimization approach )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(that is highly modular and can be easily adapted to address multiple additional issues. Our hope is that the quantitative methods )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(will assist clinical experts in developing effective policies to mitigate H1N1 using a combined arsenal of vaccines, antivirals and )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(NPIs. Specifically, a very similar analysis can be used at the international level to optimize global allocation of the WHOs )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(limited antiviral stockpile to resource-poor countries. One can substitute any stochastic model of disease transmission, at any )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(scale, for our national-scale, U.S. H1N1 model. In addition, while the optimization algorithm is particularly well suited for time-)] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(based interventions, any well-behaved policy space can be used )] TJ ET 0.267 0.267 0.267 rg BT 306.972 538.191 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 323.235 538.191 Td /F1 9.8 Tf [( . The approach should thereby facilitate a more )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(comprehensive consideration of pandemic policy options, and will perhaps confirm the efficacy of the current policy or suggest )] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(more strategic options for the future )] TJ ET 0.267 0.267 0.267 rg BT 182.864 514.381 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 199.127 514.381 Td /F1 9.8 Tf [( . The approach should thereby facilitate a more comprehensive consideration of )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(pandemic policy options, and will perhaps confirm the efficacy of the current policy or suggest more strategic options for the )] TJ ET BT 26.250 490.572 Td /F1 9.8 Tf [(future.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 453.969 Td /F4 12.0 Tf [(Supplemental Analysis)] TJ ET BT 26.250 416.817 Td /F4 12.0 Tf [(Supplemental Visualization)] TJ ET 0.271 0.267 0.267 rg BT 26.250 379.665 Td /F4 12.0 Tf [(Acknowledgments)] TJ ET BT 26.250 359.711 Td /F1 9.8 Tf [(The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the )] TJ ET BT 26.250 347.806 Td /F1 9.8 Tf [(Centers for Disease Control and Prevention. The authors thank John Tegeris at BARDA for providing up-to-date information )] TJ ET BT 26.250 335.901 Td /F1 9.8 Tf [(about the U.S. federal and state Strategic National Stockpiles of antivirals, the BARDA flu vaccine group for providing up-to-date )] TJ ET BT 26.250 323.997 Td /F1 9.8 Tf [(estimates for the availability of H1N1 vaccines, the City of Milwaukee Health Department and the Harvard Center for )] TJ ET BT 26.250 312.092 Td /F1 9.8 Tf [(Communicable Disease Dynamics for sharing unpublished data on the receipt of oseltamivir in Milwaukee. The authors )] TJ ET BT 26.250 300.187 Td /F1 9.8 Tf [(acknowledge the Texas Advanced Computing Center \(TACC\) at The University of Texas at Austin \(http://www.tacc.utexas.edu\) )] TJ ET BT 26.250 288.282 Td /F1 9.8 Tf [(for providing HPC resources that have contributed to the research results reported within this paper.)] TJ ET BT 26.250 251.680 Td /F4 12.0 Tf [(Funding Information)] TJ ET BT 26.250 231.726 Td /F1 9.8 Tf [(This work was supported by grants to LM from NIH Models of Infectious Disease Agent Study \(MIDAS\) \(U01-GM087719-01\), )] TJ ET BT 26.250 219.821 Td /F1 9.8 Tf [(the James S. McDonnell Foundation, and NSF \(DEB-0749097\) and grants to BP from CIHR \(PTL-97125 and PAP-93425\) and )] TJ ET BT 26.250 207.916 Td /F1 9.8 Tf [(the Michael Smith Foundation for Health Research.)] TJ ET BT 26.250 171.314 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 151.359 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 114.757 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 87.303 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 87.303 Td /F1 9.8 Tf [(US Centers for Disease Control \(2009\). CDC health update: Swine influenza A \(H1N1\) update: New interim )] TJ ET BT 26.250 75.398 Td /F1 9.8 Tf [(recommendations and guidance for health directors about strategic national stockpile material. )] TJ ET BT 26.250 63.493 Td /F1 9.8 Tf [(http://www.cdc.gov/h1n1flu/HAN/042609.htm.)] TJ ET BT 26.250 44.088 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 44.088 Td /F1 9.8 Tf [(Department of Health and Human Services \(2009\) National framework for 2009-H1N1 influenza preparedness and response.)] TJ ET Q q 15.000 34.207 577.500 742.793 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(thus reducing transmission )] TJ ET 0.267 0.267 0.267 rg BT 144.917 767.476 Td /F1 9.8 Tf [([26])] TJ ET 0.271 0.267 0.267 rg BT 161.180 767.476 Td /F1 9.8 Tf [(. Thus public health measures to increase the usage of antivirals for H1N1 have the potential to )] TJ ET BT 26.250 755.571 Td /F1 9.8 Tf [(slow transmission prior to the availability of H1N1 vaccine, but the impact of such measures will critically depend on the )] TJ ET BT 26.250 743.667 Td /F1 9.8 Tf [(Strategic National Stockpile distribution schedule. Although antivirals may not reduce transmission at current levels of uptake, )] TJ ET BT 26.250 731.762 Td /F1 9.8 Tf [(they can significantly reduce morbidity and mortality associated with H1N1 when used to treat potentially severe cases.)] TJ ET BT 26.250 712.357 Td /F1 9.8 Tf [(Our analysis did not consider the threat of antiviral resistance. Currently circulating strains of seasonal influenza have acquired )] TJ ET BT 26.250 700.452 Td /F1 9.8 Tf [(resistance to oseltamivir )] TJ ET 0.267 0.267 0.267 rg BT 133.529 700.452 Td /F1 9.8 Tf [([33])] TJ ET 0.271 0.267 0.267 rg BT 149.792 700.452 Td /F1 9.8 Tf [( and there is evidence that H1N1 has exhibited this resistance as well )] TJ ET 0.267 0.267 0.267 rg BT 452.179 700.452 Td /F1 9.8 Tf [([34])] TJ ET 0.271 0.267 0.267 rg BT 468.442 700.452 Td /F1 9.8 Tf [( . We also did not )] TJ ET BT 26.250 688.548 Td /F1 9.8 Tf [(incorporate the use of antivirals for prophylaxis, the future availability of vaccines, simultaneous use of NPIs like school )] TJ ET BT 26.250 676.643 Td /F1 9.8 Tf [(closures, or the option of targeting the stockpile towards particular demographic groups, all of which are likely important and )] TJ ET BT 26.250 664.738 Td /F1 9.8 Tf [(may influence the optimal policy.)] TJ ET BT 26.250 645.333 Td /F1 9.8 Tf [(From rapid genetic sequence analysis to automated syndromic surveillance systems, public health emergency response is )] TJ ET BT 26.250 633.429 Td /F1 9.8 Tf [(rapidly improving in technical capabilities both in the U.S. and worldwide; the rapid response to and characterization of the novel )] TJ ET BT 26.250 621.524 Td /F1 9.8 Tf [(pandemic influenza A \(H1N1\) virus is a testament to this. However, planning the policies of public health response to such )] TJ ET BT 26.250 609.619 Td /F1 9.8 Tf [(identified and emergent threats remains a highly non-quantitative endeavor. We present here a policy optimization approach )] TJ ET BT 26.250 597.714 Td /F1 9.8 Tf [(that is highly modular and can be easily adapted to address multiple additional issues. Our hope is that the quantitative methods )] TJ ET BT 26.250 585.810 Td /F1 9.8 Tf [(will assist clinical experts in developing effective policies to mitigate H1N1 using a combined arsenal of vaccines, antivirals and )] TJ ET BT 26.250 573.905 Td /F1 9.8 Tf [(NPIs. Specifically, a very similar analysis can be used at the international level to optimize global allocation of the WHOs )] TJ ET BT 26.250 562.000 Td /F1 9.8 Tf [(limited antiviral stockpile to resource-poor countries. One can substitute any stochastic model of disease transmission, at any )] TJ ET BT 26.250 550.095 Td /F1 9.8 Tf [(scale, for our national-scale, U.S. H1N1 model. In addition, while the optimization algorithm is particularly well suited for time-)] TJ ET BT 26.250 538.191 Td /F1 9.8 Tf [(based interventions, any well-behaved policy space can be used )] TJ ET 0.267 0.267 0.267 rg BT 306.972 538.191 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 323.235 538.191 Td /F1 9.8 Tf [( . The approach should thereby facilitate a more )] TJ ET BT 26.250 526.286 Td /F1 9.8 Tf [(comprehensive consideration of pandemic policy options, and will perhaps confirm the efficacy of the current policy or suggest )] TJ ET BT 26.250 514.381 Td /F1 9.8 Tf [(more strategic options for the future )] TJ ET 0.267 0.267 0.267 rg BT 182.864 514.381 Td /F1 9.8 Tf [([28])] TJ ET 0.271 0.267 0.267 rg BT 199.127 514.381 Td /F1 9.8 Tf [( . The approach should thereby facilitate a more comprehensive consideration of )] TJ ET BT 26.250 502.476 Td /F1 9.8 Tf [(pandemic policy options, and will perhaps confirm the efficacy of the current policy or suggest more strategic options for the )] TJ ET BT 26.250 490.572 Td /F1 9.8 Tf [(future.)] TJ ET 0.267 0.267 0.267 rg BT 26.250 453.969 Td /F4 12.0 Tf [(Supplemental Analysis)] TJ ET BT 26.250 416.817 Td /F4 12.0 Tf [(Supplemental Visualization)] TJ ET 0.271 0.267 0.267 rg BT 26.250 379.665 Td /F4 12.0 Tf [(Acknowledgments)] TJ ET BT 26.250 359.711 Td /F1 9.8 Tf [(The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the )] TJ ET BT 26.250 347.806 Td /F1 9.8 Tf [(Centers for Disease Control and Prevention. The authors thank John Tegeris at BARDA for providing up-to-date information )] TJ ET BT 26.250 335.901 Td /F1 9.8 Tf [(about the U.S. federal and state Strategic National Stockpiles of antivirals, the BARDA flu vaccine group for providing up-to-date )] TJ ET BT 26.250 323.997 Td /F1 9.8 Tf [(estimates for the availability of H1N1 vaccines, the City of Milwaukee Health Department and the Harvard Center for )] TJ ET BT 26.250 312.092 Td /F1 9.8 Tf [(Communicable Disease Dynamics for sharing unpublished data on the receipt of oseltamivir in Milwaukee. The authors )] TJ ET BT 26.250 300.187 Td /F1 9.8 Tf [(acknowledge the Texas Advanced Computing Center \(TACC\) at The University of Texas at Austin \(http://www.tacc.utexas.edu\) )] TJ ET BT 26.250 288.282 Td /F1 9.8 Tf [(for providing HPC resources that have contributed to the research results reported within this paper.)] TJ ET BT 26.250 251.680 Td /F4 12.0 Tf [(Funding Information)] TJ ET BT 26.250 231.726 Td /F1 9.8 Tf [(This work was supported by grants to LM from NIH Models of Infectious Disease Agent Study \(MIDAS\) \(U01-GM087719-01\), )] TJ ET BT 26.250 219.821 Td /F1 9.8 Tf [(the James S. McDonnell Foundation, and NSF \(DEB-0749097\) and grants to BP from CIHR \(PTL-97125 and PAP-93425\) and )] TJ ET BT 26.250 207.916 Td /F1 9.8 Tf [(the Michael Smith Foundation for Health Research.)] TJ ET BT 26.250 171.314 Td /F4 12.0 Tf [(Competing Interests)] TJ ET BT 26.250 151.359 Td /F1 9.8 Tf [(The authors have declared that no competing interests exist.)] TJ ET BT 26.250 114.757 Td /F4 12.0 Tf [(References)] TJ ET BT 26.250 87.303 Td /F1 9.8 Tf [(1.)] TJ ET BT 38.132 87.303 Td /F1 9.8 Tf [(US Centers for Disease Control \(2009\). CDC health update: Swine influenza A \(H1N1\) update: New interim )] TJ ET BT 26.250 75.398 Td /F1 9.8 Tf [(recommendations and guidance for health directors about strategic national stockpile material. )] TJ ET BT 26.250 63.493 Td /F1 9.8 Tf [(http://www.cdc.gov/h1n1flu/HAN/042609.htm.)] TJ ET BT 26.250 44.088 Td /F1 9.8 Tf [(2.)] TJ ET BT 38.132 44.088 Td /F1 9.8 Tf [(Department of Health and Human Services \(2009\) National framework for 2009-H1N1 influenza preparedness and response.)] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(7)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 552 0 obj << /Type /Annot /Subtype /Link /A 553 0 R /Border [0 0 0] /H /I /Rect [ 144.9172 766.5743 161.1803 776.4950 ] >> endobj 553 0 obj << /Type /Action >> endobj 554 0 obj << /Type /Annot /Subtype /Link /A 555 0 R /Border [0 0 0] /H /I /Rect [ 133.5292 699.5506 149.7922 709.4712 ] >> endobj 555 0 obj << /Type /Action >> endobj 556 0 obj << /Type /Annot /Subtype /Link /A 557 0 R /Border [0 0 0] /H /I /Rect [ 452.1788 699.5506 468.4418 709.4712 ] >> endobj 557 0 obj << /Type /Action >> endobj 558 0 obj << /Type /Annot /Subtype /Link /A 559 0 R /Border [0 0 0] /H /I /Rect [ 306.9720 537.2888 323.2350 547.2094 ] >> endobj 559 0 obj << /Type /Action >> endobj 560 0 obj << /Type /Annot /Subtype /Link /A 561 0 R /Border [0 0 0] /H /I /Rect [ 182.8642 513.4793 199.1273 523.3999 ] >> endobj 561 0 obj << /Type /Action >> endobj 562 0 obj << /Type /Annot /Subtype /Link /A 563 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 452.8591 157.6260 465.0691 ] >> endobj 563 0 obj << /Type /Action /S /URI /URI (http://neddimitrov.org/uploads/pdfs/currents/supplement.pdf) >> endobj 564 0 obj << /Type /Annot /Subtype /Link /A 565 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 415.7072 181.6260 427.9171 ] >> endobj 565 0 obj << /Type /Action /S /URI /URI (http://neddimitrov.org/uploads/pdfs/currents/supplemental_visualization.mp4) >> endobj 566 0 obj << /Type /Annot /Subtype /Link /A 567 0 R /Border [0 0 0] /H /I /Rect [ 144.9172 766.5743 161.1803 776.4950 ] >> endobj 567 0 obj << /Type /Action >> endobj 568 0 obj << /Type /Annot /Subtype /Link /A 569 0 R /Border [0 0 0] /H /I /Rect [ 133.5292 699.5506 149.7922 709.4712 ] >> endobj 569 0 obj << /Type /Action >> endobj 570 0 obj << /Type /Annot /Subtype /Link /A 571 0 R /Border [0 0 0] /H /I /Rect [ 452.1788 699.5506 468.4418 709.4712 ] >> endobj 571 0 obj << /Type /Action >> endobj 572 0 obj << /Type /Annot /Subtype /Link /A 573 0 R /Border [0 0 0] /H /I /Rect [ 306.9720 537.2888 323.2350 547.2094 ] >> endobj 573 0 obj << /Type /Action >> endobj 574 0 obj << /Type /Annot /Subtype /Link /A 575 0 R /Border [0 0 0] /H /I /Rect [ 182.8642 513.4793 199.1273 523.3999 ] >> endobj 575 0 obj << /Type /Action >> endobj 576 0 obj << /Type /Annot /Subtype /Link /A 577 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 452.8591 157.6260 465.0691 ] >> endobj 577 0 obj << /Type /Action /S /URI /URI (http://neddimitrov.org/uploads/pdfs/currents/supplement.pdf) >> endobj 578 0 obj << /Type /Annot /Subtype /Link /A 579 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 415.7072 181.6260 427.9171 ] >> endobj 579 0 obj << /Type /Action /S /URI /URI (http://neddimitrov.org/uploads/pdfs/currents/supplemental_visualization.mp4) >> endobj 580 0 obj << /Type /Annot /Subtype /Link /A 581 0 R /Border [0 0 0] /H /I /Rect [ 144.9172 766.5743 161.1803 776.4950 ] >> endobj 581 0 obj << /Type /Action >> endobj 582 0 obj << /Type /Annot /Subtype /Link /A 583 0 R /Border [0 0 0] /H /I /Rect [ 133.5292 699.5506 149.7922 709.4712 ] >> endobj 583 0 obj << /Type /Action >> endobj 584 0 obj << /Type /Annot /Subtype /Link /A 585 0 R /Border [0 0 0] /H /I /Rect [ 452.1788 699.5506 468.4418 709.4712 ] >> endobj 585 0 obj << /Type /Action >> endobj 586 0 obj << /Type /Annot /Subtype /Link /A 587 0 R /Border [0 0 0] /H /I /Rect [ 306.9720 537.2888 323.2350 547.2094 ] >> endobj 587 0 obj << /Type /Action >> endobj 588 0 obj << /Type /Annot /Subtype /Link /A 589 0 R /Border [0 0 0] /H /I /Rect [ 182.8642 513.4793 199.1273 523.3999 ] >> endobj 589 0 obj << /Type /Action >> endobj 590 0 obj << /Type /Annot /Subtype /Link /A 591 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 452.8591 157.6260 465.0691 ] >> endobj 591 0 obj << /Type /Action /S /URI /URI (http://neddimitrov.org/uploads/pdfs/currents/supplement.pdf) >> endobj 592 0 obj << /Type /Annot /Subtype /Link /A 593 0 R /Border [0 0 0] /H /I /Rect [ 26.2500 415.7072 181.6260 427.9171 ] >> endobj 593 0 obj << /Type /Action /S /URI /URI (http://neddimitrov.org/uploads/pdfs/currents/supplemental_visualization.mp4) >> endobj 594 0 obj << /Type /Page /Parent 3 0 R /Contents 595 0 R >> endobj 595 0 obj << /Length 21721 >> stream 0.271 0.267 0.267 rg q 15.000 29.977 577.500 747.023 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 759.976 Td /F1 9.8 Tf [(Department of Homeland Security \(2007\). 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PLoS Medicine 3: e387.)] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 646.643 Td /F1 9.8 Tf [(Germann T, Kadau K, Longini I, Mackan C \(2006\) Mitigation strategies for pandemic influenza in the united states. )] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(Proceedings of the National Academy of Sciences 103: 5935-5940.)] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 615.333 Td /F1 9.8 Tf [(Kocsis L, Szepesvri C \(2006\) Bandit based monte-carlo planning. Machine Learning: ECML 2006 282-293.)] TJ ET BT 26.250 595.929 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 595.929 Td /F1 9.8 Tf [(Auer P, Cesa-Bianchi N, Fischer P \(2002\) Finite-time analysis of the multiarmed bandit problem. Machine Learning 47: 235-)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(256.)] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 564.619 Td /F1 9.8 Tf [(Bureau of Transportation Statistics \(2008\). Airport master coordinate data. http://www.transtats.bts.gov/Fields.asp?Table )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(ID=288.)] TJ ET BT 26.250 533.310 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 533.310 Td /F1 9.8 Tf [(Census Bureau \(2000\). About metropolitan and micropolitan statistical areas. )] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(http://www.census.gov/population/www/metroareas/aboutmetro.html.)] TJ ET BT 26.250 502.000 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 502.000 Td /F1 9.8 Tf [(Census Bureau \(2000\). County-to-county worker flow files. )] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(http://www.census.gov/population/www/cen2000/commuting/index.html.)] TJ ET BT 26.250 470.691 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 470.691 Td /F1 9.8 Tf [(Bureau of Transportation Statistics \(2007\). Origin and destination survey, all quarters of 2007. )] TJ ET BT 26.250 458.786 Td /F1 9.8 Tf [(http://www.transtats.bts.gov/Fields.asp?Table ID=289.)] TJ ET BT 26.250 439.381 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 439.381 Td /F1 9.8 Tf [(Keeling MJ, Rohani P \(2008\) Modeling Infectious Diseases. Princeton University Press.)] TJ ET BT 26.250 419.976 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 419.976 Td /F1 9.8 Tf [(Schuchat A \(2009\). CDC telebriefing on investigation of human cases of novel influenza A \(H1N1\). )] TJ ET BT 26.250 408.072 Td /F1 9.8 Tf [(http://www.cdc.gov/media/transcripts/2009/t090626.htm.)] TJ ET BT 26.250 388.667 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 388.667 Td /F1 9.8 Tf [(Pourbohloul B, Ahued A, Davoudi B, Meza R, Meyers L, et al. \(2009\) Initial human transmission dynamics of a novel swine-)] TJ ET BT 26.250 376.762 Td /F1 9.8 Tf [(origin influenza A \(H1N1\) virus \(S-OIV\) in North America. Influenza and Other Respiratory Viruses.)] TJ ET BT 26.250 357.357 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 357.357 Td /F1 9.8 Tf [(Fraser C, Donnelly C, Cauchemez S, Hanage W, Van Kerkhove M, et al. \(2009\) Pandemic potential of a strain of influenza )] TJ ET BT 26.250 345.453 Td /F1 9.8 Tf [(A \(H1N1\): early findings. Science 5934: 1557-1561.)] TJ ET BT 26.250 326.048 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 326.048 Td /F1 9.8 Tf [(US Centers for Disease Control \(2009\). Interim guidance for clinicians on identifying and caring for patients with swine-)] TJ ET BT 26.250 314.143 Td /F1 9.8 Tf [(origin influenza A \(H1N1\) virus infection. http://www.cdc.gov/h1n1flu/identifyingpatients.htm#incubationperiod.)] TJ ET BT 26.250 294.738 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 294.738 Td /F1 9.8 Tf [(Lee V, Chen M \(2007\) Effectiveness of neuraminidase inhibitors for preventing staff absenteeism during pandemic )] TJ ET BT 26.250 282.834 Td /F1 9.8 Tf [(influenza. Emerging Infectious Diseases 13: 449-457.)] TJ ET BT 26.250 263.429 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 263.429 Td /F1 9.8 Tf [(McCaw J, McVernon J \(2007\) Prophylaxis or treatment? Optimal use of an antiviral stockpile during an influenza pandemic. )] TJ ET BT 26.250 251.524 Td /F1 9.8 Tf [(Mathematical Biosciences 209: 336-360.)] TJ ET BT 26.250 232.119 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 232.119 Td /F1 9.8 Tf [(Lee V, Phua K, Chen M, Chow A, Stefan M, et al. \(2006\) Economics of neuraminidase inhibitor stockpiling for pandemic )] TJ ET BT 26.250 220.215 Td /F1 9.8 Tf [(influenza, Singapore. Emerging Infectious Diseases 12: 95-102.)] TJ ET BT 26.250 200.810 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 200.810 Td /F1 9.8 Tf [(Doyle A, Bonmarin I, Levy-Bruhl D, Strat Y, Desenclos JC \(2006\) Influenza pandemic preparedness in France: modelling )] TJ ET BT 26.250 188.905 Td /F1 9.8 Tf [(the impact of interventions. Journal of Epidemiology and Community Health 60: 399-404.)] TJ ET BT 26.250 169.500 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 169.500 Td /F1 9.8 Tf [(Barnes B, Glass K, Becker N \(2007\) The role of health care workers and antiviral drugs in the control of pandemic influenza. )] TJ ET BT 26.250 157.596 Td /F1 9.8 Tf [(Mathematical Biosciences 209: 403-416.)] TJ ET BT 26.250 138.191 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 138.191 Td /F1 9.8 Tf [(Hota S, McGeer A \(2007\) Antivirals and the control of influenza outbreaks. Clinical Infectious Diseases 45: 1362-1368.)] TJ ET BT 26.250 118.786 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 118.786 Td /F1 9.8 Tf [(Lipsitch M, Cohen T, Murray M, Levin B \(2007\) Antiviral resistance and the control of pandemic influenza. PLoS Medicine 4: )] TJ ET BT 26.250 106.881 Td /F1 9.8 Tf [(e15.)] TJ ET BT 26.250 87.477 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 87.477 Td /F1 9.8 Tf [(Smieja M, Petrich A, Luinstra K, Chong S, Carruthers S, et al. \(2009\) Viral load testing of influenza A/california 2009 \(H1N1, )] TJ ET BT 26.250 75.572 Td /F1 9.8 Tf [(swine flu\) in serial nasopharyngeal or self-collected nasal swabs. International Society for Chemotherapy and Infections )] TJ ET BT 26.250 63.667 Td /F1 9.8 Tf [(meeting in Toronto, Canada.)] TJ ET BT 26.250 44.262 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 44.262 Td /F1 9.8 Tf [(Azadivar F \(1999\) Simulation optimization methodologies. Proceedings of the 31st conference on Winter simulation : )] TJ ET Q q 15.000 29.977 577.500 747.023 re W n 0.271 0.267 0.267 rg BT 26.250 759.976 Td /F1 9.8 Tf [(3.)] TJ ET BT 38.132 759.976 Td /F1 9.8 Tf [(Department of Homeland Security \(2007\). Homeland security presidential directive 21. http://www.dhs.gov/xabout/laws/gc )] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(1219263961449.shtm.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(4.)] TJ ET BT 38.132 728.667 Td /F1 9.8 Tf [(Longini I, Halloran M, Nizam A, Yang Y \(2004\) Containing pandemic influenza with antiviral agents. American Journal of )] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(Epidemiology 159: 623-633.)] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(5.)] TJ ET BT 38.132 697.357 Td /F1 9.8 Tf [(Ferguson N, Cummings D, Cauchemez S, Fraser C, Riley S, et al. \(2005\) Strategies for containing an emerging influenza )] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(pandemic in Southeast Asia. Nature 437: 204-214.)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(6.)] TJ ET BT 38.132 666.048 Td /F1 9.8 Tf [(Bansal S, Pourbohloul B, Meyers L \(2006\) A comparative analysis of influenza vaccination programs. PLoS Medicine 3: e387.)] TJ ET BT 26.250 646.643 Td /F1 9.8 Tf [(7.)] TJ ET BT 38.132 646.643 Td /F1 9.8 Tf [(Germann T, Kadau K, Longini I, Mackan C \(2006\) Mitigation strategies for pandemic influenza in the united states. )] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(Proceedings of the National Academy of Sciences 103: 5935-5940.)] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(8.)] TJ ET BT 38.132 615.333 Td /F1 9.8 Tf [(Kocsis L, Szepesvri C \(2006\) Bandit based monte-carlo planning. Machine Learning: ECML 2006 282-293.)] TJ ET BT 26.250 595.929 Td /F1 9.8 Tf [(9.)] TJ ET BT 38.132 595.929 Td /F1 9.8 Tf [(Auer P, Cesa-Bianchi N, Fischer P \(2002\) Finite-time analysis of the multiarmed bandit problem. Machine Learning 47: 235-)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(256.)] TJ ET BT 26.250 564.619 Td /F1 9.8 Tf [(10.)] TJ ET BT 43.553 564.619 Td /F1 9.8 Tf [(Bureau of Transportation Statistics \(2008\). Airport master coordinate data. http://www.transtats.bts.gov/Fields.asp?Table )] TJ ET BT 26.250 552.714 Td /F1 9.8 Tf [(ID=288.)] TJ ET BT 26.250 533.310 Td /F1 9.8 Tf [(11.)] TJ ET BT 43.553 533.310 Td /F1 9.8 Tf [(Census Bureau \(2000\). About metropolitan and micropolitan statistical areas. )] TJ ET BT 26.250 521.405 Td /F1 9.8 Tf [(http://www.census.gov/population/www/metroareas/aboutmetro.html.)] TJ ET BT 26.250 502.000 Td /F1 9.8 Tf [(12.)] TJ ET BT 43.553 502.000 Td /F1 9.8 Tf [(Census Bureau \(2000\). County-to-county worker flow files. )] TJ ET BT 26.250 490.095 Td /F1 9.8 Tf [(http://www.census.gov/population/www/cen2000/commuting/index.html.)] TJ ET BT 26.250 470.691 Td /F1 9.8 Tf [(13.)] TJ ET BT 43.553 470.691 Td /F1 9.8 Tf [(Bureau of Transportation Statistics \(2007\). Origin and destination survey, all quarters of 2007. )] TJ ET BT 26.250 458.786 Td /F1 9.8 Tf [(http://www.transtats.bts.gov/Fields.asp?Table ID=289.)] TJ ET BT 26.250 439.381 Td /F1 9.8 Tf [(14.)] TJ ET BT 43.553 439.381 Td /F1 9.8 Tf [(Keeling MJ, Rohani P \(2008\) Modeling Infectious Diseases. Princeton University Press.)] TJ ET BT 26.250 419.976 Td /F1 9.8 Tf [(15.)] TJ ET BT 43.553 419.976 Td /F1 9.8 Tf [(Schuchat A \(2009\). CDC telebriefing on investigation of human cases of novel influenza A \(H1N1\). )] TJ ET BT 26.250 408.072 Td /F1 9.8 Tf [(http://www.cdc.gov/media/transcripts/2009/t090626.htm.)] TJ ET BT 26.250 388.667 Td /F1 9.8 Tf [(16.)] TJ ET BT 43.553 388.667 Td /F1 9.8 Tf [(Pourbohloul B, Ahued A, Davoudi B, Meza R, Meyers L, et al. \(2009\) Initial human transmission dynamics of a novel swine-)] TJ ET BT 26.250 376.762 Td /F1 9.8 Tf [(origin influenza A \(H1N1\) virus \(S-OIV\) in North America. Influenza and Other Respiratory Viruses.)] TJ ET BT 26.250 357.357 Td /F1 9.8 Tf [(17.)] TJ ET BT 43.553 357.357 Td /F1 9.8 Tf [(Fraser C, Donnelly C, Cauchemez S, Hanage W, Van Kerkhove M, et al. \(2009\) Pandemic potential of a strain of influenza )] TJ ET BT 26.250 345.453 Td /F1 9.8 Tf [(A \(H1N1\): early findings. Science 5934: 1557-1561.)] TJ ET BT 26.250 326.048 Td /F1 9.8 Tf [(18.)] TJ ET BT 43.553 326.048 Td /F1 9.8 Tf [(US Centers for Disease Control \(2009\). Interim guidance for clinicians on identifying and caring for patients with swine-)] TJ ET BT 26.250 314.143 Td /F1 9.8 Tf [(origin influenza A \(H1N1\) virus infection. http://www.cdc.gov/h1n1flu/identifyingpatients.htm#incubationperiod.)] TJ ET BT 26.250 294.738 Td /F1 9.8 Tf [(19.)] TJ ET BT 43.553 294.738 Td /F1 9.8 Tf [(Lee V, Chen M \(2007\) Effectiveness of neuraminidase inhibitors for preventing staff absenteeism during pandemic )] TJ ET BT 26.250 282.834 Td /F1 9.8 Tf [(influenza. Emerging Infectious Diseases 13: 449-457.)] TJ ET BT 26.250 263.429 Td /F1 9.8 Tf [(20.)] TJ ET BT 43.553 263.429 Td /F1 9.8 Tf [(McCaw J, McVernon J \(2007\) Prophylaxis or treatment? Optimal use of an antiviral stockpile during an influenza pandemic. )] TJ ET BT 26.250 251.524 Td /F1 9.8 Tf [(Mathematical Biosciences 209: 336-360.)] TJ ET BT 26.250 232.119 Td /F1 9.8 Tf [(21.)] TJ ET BT 43.553 232.119 Td /F1 9.8 Tf [(Lee V, Phua K, Chen M, Chow A, Stefan M, et al. \(2006\) Economics of neuraminidase inhibitor stockpiling for pandemic )] TJ ET BT 26.250 220.215 Td /F1 9.8 Tf [(influenza, Singapore. Emerging Infectious Diseases 12: 95-102.)] TJ ET BT 26.250 200.810 Td /F1 9.8 Tf [(22.)] TJ ET BT 43.553 200.810 Td /F1 9.8 Tf [(Doyle A, Bonmarin I, Levy-Bruhl D, Strat Y, Desenclos JC \(2006\) Influenza pandemic preparedness in France: modelling )] TJ ET BT 26.250 188.905 Td /F1 9.8 Tf [(the impact of interventions. Journal of Epidemiology and Community Health 60: 399-404.)] TJ ET BT 26.250 169.500 Td /F1 9.8 Tf [(23.)] TJ ET BT 43.553 169.500 Td /F1 9.8 Tf [(Barnes B, Glass K, Becker N \(2007\) The role of health care workers and antiviral drugs in the control of pandemic influenza. )] TJ ET BT 26.250 157.596 Td /F1 9.8 Tf [(Mathematical Biosciences 209: 403-416.)] TJ ET BT 26.250 138.191 Td /F1 9.8 Tf [(24.)] TJ ET BT 43.553 138.191 Td /F1 9.8 Tf [(Hota S, McGeer A \(2007\) Antivirals and the control of influenza outbreaks. Clinical Infectious Diseases 45: 1362-1368.)] TJ ET BT 26.250 118.786 Td /F1 9.8 Tf [(25.)] TJ ET BT 43.553 118.786 Td /F1 9.8 Tf [(Lipsitch M, Cohen T, Murray M, Levin B \(2007\) Antiviral resistance and the control of pandemic influenza. PLoS Medicine 4: )] TJ ET BT 26.250 106.881 Td /F1 9.8 Tf [(e15.)] TJ ET BT 26.250 87.477 Td /F1 9.8 Tf [(26.)] TJ ET BT 43.553 87.477 Td /F1 9.8 Tf [(Smieja M, Petrich A, Luinstra K, Chong S, Carruthers S, et al. \(2009\) Viral load testing of influenza A/california 2009 \(H1N1, )] TJ ET BT 26.250 75.572 Td /F1 9.8 Tf [(swine flu\) in serial nasopharyngeal or self-collected nasal swabs. International Society for Chemotherapy and Infections )] TJ ET BT 26.250 63.667 Td /F1 9.8 Tf [(meeting in Toronto, Canada.)] TJ ET BT 26.250 44.262 Td /F1 9.8 Tf [(27.)] TJ ET BT 43.553 44.262 Td /F1 9.8 Tf [(Azadivar F \(1999\) Simulation optimization methodologies. Proceedings of the 31st conference on Winter simulation : )] TJ ET Q q 0.000 0.000 0.000 rg BT 291.710 19.825 Td /F1 11.0 Tf [(8)] TJ ET BT 25.000 19.825 Td /F1 11.0 Tf [(PLOS Currents Influenza)] TJ ET Q endstream endobj 596 0 obj << /Type /Page /Parent 3 0 R /Contents 597 0 R >> endobj 597 0 obj << /Length 6283 >> stream 0.271 0.267 0.267 rg q 15.000 554.738 577.500 222.262 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(93100.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 748.071 Td /F1 9.8 Tf [(Coquelin P, Munos R \(2007\) Bandit algorithms for tree search. 23rd Conference on Uncertainty in Artificial Intelligence.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 728.667 Td /F1 9.8 Tf [(Mannor S, Tsitsiklis J \(2004\) The sample complexity of exploration in the multi-armed bandit problem. Journal of Machine )] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(Learning Research 5: 623648.)] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 697.357 Td /F1 9.8 Tf [(Dar E, Mannor S, Mansour Y \(2002\) Pac bounds for multi-armed bandit and markov decision processes. Proceedings of the )] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(15th Annual Conference on Computational Learning Theory : 255270.)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 666.048 Td /F1 9.8 Tf [(Gelly S, Wang Y \(2006\) Exploration exploitation in Go: UCT for Monte-Carlo Go. 20th annual Conference on Neural )] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(Information Processing Systems.)] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 634.738 Td /F1 9.8 Tf [(Lipsitch M \(2009\). personal communication.)] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 615.333 Td /F1 9.8 Tf [(AC H, J E, YM D, P I, TG B, et al. \(2009\) Emergence and spread of oseltamivir-resistant A\(H1N1\) influenza viruses in )] TJ ET BT 26.250 603.429 Td /F1 9.8 Tf [(oceania, south east asia and south africa. Antiviral Research 83: 90-93.)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 584.024 Td /F1 9.8 Tf [(World Health Organization \(2009\). Pandemic \(H1N1\) 2009 briefing note 1: Viruses resistant to oseltamivir \(tamiflu\) )] TJ ET BT 26.250 572.119 Td /F1 9.8 Tf [(identified. http://www.who.int/csr/disease/swineflu/notes/h1n1 antiviral resistance 20090708/en/index.html.)] TJ ET Q q 15.000 554.738 577.500 222.262 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(93100.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 748.071 Td /F1 9.8 Tf [(Coquelin P, Munos R \(2007\) Bandit algorithms for tree search. 23rd Conference on Uncertainty in Artificial Intelligence.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 728.667 Td /F1 9.8 Tf [(Mannor S, Tsitsiklis J \(2004\) The sample complexity of exploration in the multi-armed bandit problem. Journal of Machine )] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(Learning Research 5: 623648.)] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 697.357 Td /F1 9.8 Tf [(Dar E, Mannor S, Mansour Y \(2002\) Pac bounds for multi-armed bandit and markov decision processes. Proceedings of the )] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(15th Annual Conference on Computational Learning Theory : 255270.)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 666.048 Td /F1 9.8 Tf [(Gelly S, Wang Y \(2006\) Exploration exploitation in Go: UCT for Monte-Carlo Go. 20th annual Conference on Neural )] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(Information Processing Systems.)] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 634.738 Td /F1 9.8 Tf [(Lipsitch M \(2009\). personal communication.)] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 615.333 Td /F1 9.8 Tf [(AC H, J E, YM D, P I, TG B, et al. \(2009\) Emergence and spread of oseltamivir-resistant A\(H1N1\) influenza viruses in )] TJ ET BT 26.250 603.429 Td /F1 9.8 Tf [(oceania, south east asia and south africa. Antiviral Research 83: 90-93.)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 584.024 Td /F1 9.8 Tf [(World Health Organization \(2009\). Pandemic \(H1N1\) 2009 briefing note 1: Viruses resistant to oseltamivir \(tamiflu\) )] TJ ET BT 26.250 572.119 Td /F1 9.8 Tf [(identified. http://www.who.int/csr/disease/swineflu/notes/h1n1 antiviral resistance 20090708/en/index.html.)] TJ ET Q q 15.000 554.738 577.500 222.262 re W n 0.271 0.267 0.267 rg BT 26.250 767.476 Td /F1 9.8 Tf [(93100.)] TJ ET BT 26.250 748.071 Td /F1 9.8 Tf [(28.)] TJ ET BT 43.553 748.071 Td /F1 9.8 Tf [(Coquelin P, Munos R \(2007\) Bandit algorithms for tree search. 23rd Conference on Uncertainty in Artificial Intelligence.)] TJ ET BT 26.250 728.667 Td /F1 9.8 Tf [(29.)] TJ ET BT 43.553 728.667 Td /F1 9.8 Tf [(Mannor S, Tsitsiklis J \(2004\) The sample complexity of exploration in the multi-armed bandit problem. Journal of Machine )] TJ ET BT 26.250 716.762 Td /F1 9.8 Tf [(Learning Research 5: 623648.)] TJ ET BT 26.250 697.357 Td /F1 9.8 Tf [(30.)] TJ ET BT 43.553 697.357 Td /F1 9.8 Tf [(Dar E, Mannor S, Mansour Y \(2002\) Pac bounds for multi-armed bandit and markov decision processes. Proceedings of the )] TJ ET BT 26.250 685.452 Td /F1 9.8 Tf [(15th Annual Conference on Computational Learning Theory : 255270.)] TJ ET BT 26.250 666.048 Td /F1 9.8 Tf [(31.)] TJ ET BT 43.553 666.048 Td /F1 9.8 Tf [(Gelly S, Wang Y \(2006\) Exploration exploitation in Go: UCT for Monte-Carlo Go. 20th annual Conference on Neural )] TJ ET BT 26.250 654.143 Td /F1 9.8 Tf [(Information Processing Systems.)] TJ ET BT 26.250 634.738 Td /F1 9.8 Tf [(32.)] TJ ET BT 43.553 634.738 Td /F1 9.8 Tf [(Lipsitch M \(2009\). personal communication.)] TJ ET BT 26.250 615.333 Td /F1 9.8 Tf [(33.)] TJ ET BT 43.553 615.333 Td /F1 9.8 Tf [(AC H, J E, YM D, P I, TG B, et al. \(2009\) Emergence and spread of oseltamivir-resistant A\(H1N1\) influenza viruses in )] TJ ET BT 26.250 603.429 Td /F1 9.8 Tf [(oceania, south east asia and south africa. Antiviral Research 83: 90-93.)] TJ ET BT 26.250 584.024 Td /F1 9.8 Tf [(34.)] TJ ET BT 43.553 584.024 Td /F1 9.8 Tf [(World Health Organization \(2009\). 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